MORRIS SHEPPARD ARNOLD, Circuit Judge.

In 1992, a jury convicted John Martin in Arkansas state court of kidnapping and first-degree murder. On direct appeal, he argued that there was insufficient corroboration under Arkansas law of the testimony of his alleged accomplice, see Ark.Code Ann. § 16-89-lll(e)(l), and therefore that the evidence was insufficient under Arkansas law to sustain his convictions. He also argued that the state trial court improperly refused to instruct the jury on the lesser included offense of second-degree murder.

The state appeals court held that Mr. Martin’s trial lawyer had failed to make an adequately specific motion for a directed verdict at the close of the evidence, see Ark. R.Crim. P. 36.21(b), and therefore that Mr. Martin had waived the issue of the sufficiency of the evidence. See Martin v. State, 46 Ark.App. 276, 879 S.W.2d 470, 472 (1994). The state appeals court also held that because Mr. Martin’s defense was that he was not even in Arkansas at the time of the crime, there was no rational basis for allowing a jury instruction on second-degree murder. See id., 879 S.W.2d at 472-73. The state appeals court subsequently denied Mr. Martin’s petition for rehearing. See Martin v. State, 46 Ark.App. 276, 883 S.W.2d 864 (1994) (en banc).

In late 1994, Mr. Martin filed in federal district court for habeas corpus relief under 28 U.S.C. § 2254(a). In his habeas petition, Mr. Martin alleged, first, that his state trial lawyer was ineffective to a constitutionally significant degree in failing to move specifically enough for a directed verdict at the close of the evidence and, second, that the trial court denied him due process by refusing to instruct the jury on second-degree murder.

A magistrate recommended that Mr. Martin’s petition be denied. With respect to the issue of ineffective assistance of counsel, the magistrate assumed that Mr. Martin’s trial lawyer’s performance was not objectively reasonable under Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 2064-65, 80 L.Ed.2d 674 (1984). The magistrate noted, however, that the state trial court denied the motion for a directed verdict that Mr. Martin’s lawyer made when the state rested (before the defense presented its only witness) and concluded from that action that no matter how Mr. Martin’s lawyer might have phrased his motion for a directed verdict at the close of the evidence, the state trial court would have denied that motion.

The magistrate then went on to discuss the sufficiency of the corroborating evidence and concluded that if the state appeals court had considered the legal issue of sufficiency, that court would have upheld the trial court’s denial of the motion for a directed verdict. The magistrate reasoned, therefore, that Mr. Martin suffered no prejudice from his trial lawyer’s action. See id. at 692, 104 S.Ct. at 2067. In other words, the magistrate believed that there was no “reasonable probability” that if Mr. Martin’s trial lawyer had made a proper motion at the close of the evidence, “the result of the proceeding would have been different” — i.e., that the state appeals court would have reversed the trial court and dismissed the case as legally insufficient. Id. at 694, 104 S.Ct. at 2068. With respect to the jury instruction on second-degree murder, the magistrate concluded that the state trial court’s refusal to give that instruction was not such a deprivation as to amount to a violation of due process.

The district court reviewed the record de novo and adopted the report and recommendation of the magistrate. The district court also held, independently, that the motion for a directed verdict that Mr. Martin’s lawyer made at the close of the evidence was adequate under Arkansas law and that Mr. Martin’s trial lawyer’s performance was, therefore, objectively reasonable. See id. at 687-88, 104 S.Ct. at 2064-65. Mr. Martin ap *214 peals. We affirm the judgment of the district court. 1

For the purposes of this opinion, we assume, without holding, that Mr. Martin’s lawyer failed to preserve properly the issue of the sufficiency of the evidence against Mr. Martin. We further assume, without holding, that that failure was not objectively reasonable under Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 2064-65, 80 L.Ed.2d 674 (1984). We turn, then, to the question of whether that failure was so serious that “there is a reasonable probability that, but for counsel’s unprofessional error[ ], the result of the proceeding would have been different.” Id. at 694, 104 S.Ct. at 2068. In other words, we consider whether there is a reasonable probability that the state appeals court would have reversed the state trial court’s denial of Mr. Martin’s lawyer’s motion for a directed verdict if the state appeals court had evaluated the sufficiency of the evidence as a legal matter.

Under Arkansas law, a person may not be convicted of a felony solely on the basis of the testimony of an accomplice. See Ark.Code Ann. § 16-89-111(e)(1). There must be “other evidence tending to connect the defendant with the commission of the offense.” Id. The corroborating evidence “must connect the accused with the crime and be independent of the evidence given by the accomplice.... The test for determining the sufficiency of the corroborating evidence is whether, if the accomplice’s testimony were eliminated from the case, the other evidence independently establishes the crime and tends to connect the accused with its commission.” Sanders v. State, 310 Ark. 510, 838 S.W.2d 359, 360 (1992). The corroborating evidence must be “stronger evidence than that which merely raises a suspicion of guilt.... However, it is something less than that evidence necessary[,] in and of itself, to sustain a conviction.” Henderson v. State, 279 Ark. 435, 652 S.W.2d 16, 19-20 (1983). When an accomplice’s testimony “is corroborated as to particular material facts, the fact-finder can infer [that] the accomplice spoke the truth as to all.” Franklin v. State, 311 Ark. 601, 845 S.W.2d 525, 529 (1993). With these principles in mind, we recount the testimony of Mr. Martin’s alleged accomplice and the corroboration provided for that testimony.

II.

The alleged accomplice was Mr. Martin’s nephew, Adell Henry. According to Mr. Henry’s testimony, he and Mr. Martin drove Mr. Martin’s gold Cadillac from Lawton, Oklahoma, where they lived in the same house, to Little Rock, Arkansas, on October 11, 1991. The trip was Mr. Martin’s idea. They arrived late (around 11:00 p.m. or midnight), “rode around town,” and then went to a convenience store, where Mr. Henry called a former girlfriend. They went to the former girlfriend’s home about two hours after they arrived in Little Rock. Mr. Henry went inside and stayed until shortly before 7:00 a.m; Mr. Martin remained in the car (although he had family who lived only 10 blocks away). In corroboration, Mr. Henry’s former girlfriend testified that he called her in Little Rock on October 12, 1991, around 2:30 a.m., came over shortly thereafter, and stayed till about 6:00 a.m.

According to Mr. Henry, after he returned to the car that morning, Mr. Martin drove to the college where his wife, Felicia Martin, from whom he was estranged, worked. His wife drove into the college parking lot at approximately the same time. Mr. Martin parked and went over to talk to Mrs. Martin in her ear. After a short time, Mrs. Martin went inside the building where she worked but then came out and talked again with Mr. Martin. Both walked over to the gold Cadillac, where Mr. Henry was waiting in the front seat. Mr. and Mrs. Martin talked momentarily by the back door on the passenger’s side. Mr. Martin then opened that door, pushed Mrs. Martin into the car, and told Mr. Henry to drive off.

*215 In corroboration, a co-worker of Mrs. Martin’s testified that he arrived at the college on October 12,1991, about 7:05 a.m. He saw Mrs. Martin clock in about 7:10 a.m. Shortly afterward, he saw Mrs. Martin sitting in her car with a black man who “looked large.” He also saw a gold Cadillac nearby and identified a picture of Mr. Martin’s car as the one he saw. He later saw Mrs. Martin standing by the gold Cadillac. The next time he looked, both Mrs. Martin and the gold Cadillac were gone, although her car remained in the parking lot. He stated that Mrs. Martin was wearing glasses that morning and left a coin purse and a cup of coffee at her workplace.

Also in corroboration, Mrs. Martin’s great-aunt testified that one of Mrs. Martin’s coworkers called her about 9:00 a.m. on October 12, 1991, to say that Mrs. Martin was missing. The great-aunt stated that Mrs. Martin always wore glasses and “said she couldn’t see without them.” The great-aunt identified a pair of glasses as those belonging to Mrs. Martin. A man who worked in the housekeeping department at the college identified those glasses as the ones he found between 9:00 a.m. and 10:00 a.m. on October 12, 1991, near a curb behind Mrs. Martin’s workplace.

According to Mr. Henry, Mrs. Martin “was trying to get up [in the car], and [Mr. Martin] was laying on top of her.” A few blocks later, Mr. Henry heard Mbs. Martin “gasping for air” and “choking.” Mr. Henry further stated that Mb. Martin subsequently told him to pull over; Mr. Martin began driving; Mr. Henry heard nothing more from the back seat.

In corroboration, the medical examiner who autopsied Mrs. Martin testified that she died from being strangled, specifically, that some sort of ligature was pulled horizontally across her neck from front to back, cutting off the blood flow from her brain. He stated that such strangulation, which requires “surprisingly little” pressure, causes unconsciousness within “only an order of seconds,” and induces death in “only a matter of a few seconds more.” He further remarked that Mrs. Martin had abrasions from pressure on the front of her neck that were “consistent with ... [some] kind of a struggle” by Mbs. Martin and that she had bleeding deep inside her neck and lacerations inside her lips of the type “commonly” made by a fist.

Mb. Henry testified that Mb. Martin eventually stopped, got out of the ear and told Mb. Henry to get out, and handed some gloves to Mb. Henry, directing him to help remove Mbs. Martin from the car. Mb. Martin also put on gloves. Mbs. Martin was not moving and said nothing. Although she was wearing glasses when she first talked with Mb. Martin at the college, she was not wearing glasses when Mb. Martin and Mb. Henry took her from the car. Mb. Martin and Mb. Henry put Mbs. Martin’s body “in some weeds.”

In corroboration, a Lawton, Oklahoma, police detective testified that when he searched Mb. Martin’s ear on October 13, 1991, he found two pairs of leather gloves “stuffed in a side pocket in the rear back seat compartment.” He also testified that he found a gold chain “in a small console in between the seats.” A Little Rock police detective testified that Mbs. Martin was reported missing shortly after noon on October 12, 1991, and that her body was found a few hours later. The police made plaster casts of tíre tread marks where her body was found; the crime laboratory determined that those marks were “similar” to the tire tread pattern on Mb. Martin’s car. The medical examiner testified that the marks on Mbs. Martin’s neck were “consistent with” the pattern of the gold chain that was found in Mb. Martin’s car.

Finally, Mb. Henry testified that he drove Mb. Martin back to Oklahoma. On the way, Mb. Martin directed Mb. Henry to say that they had been to Tulsa, “if anybody asks.” An Oklahoma state trooper stopped Mb. Henry for speeding about noon and gave him a ticket. When they got back to Lawton, Mb. Martin washed the car. In corroboration, an Oklahoma state trooper testified that he stopped Mb. Henry for speeding around noon on October 12,1991, and that there was “a rather large shouldered” black man who “appeared a little nervous” in the car with Mb. Henry. The state trooper also testified that one route from Little Rock to Lawton, Oklahoma, would be on the highway where *216 he stopped Mr. Henry and that a person who left Little Rock around 7:30 a.m. or 8:00 a.m. “could approximately be,” by noon, in the area where he stopped Mr. Henry. He identified Mr. Henry from a photo spread as the driver whom he stopped and ticketed about noon.

“Corroboration may [also] be furnished by the acts, conduct, [or] declarations ... of the accused.” Henderson v. State, 279 Ark. 435, 652 S.W.2d 16, 20 (1983). “A jury may consider and give weight to any ... improbable, and contradictory statements made by an accused explaining suspicious circumstances.” Watson v. State, 290 Ark. 484, 720 S.W.2d 310, 312 (1986). “False statements to the police ... may constitute corroborating evidence.” Henderson, 652 S.W.2d at 20. It is “settled beyond question,” moreover, that “a party’s attempt to fabricate evidence is admissible ... as proof relevant to show his own belief that his case is weak. As one court has said, in a case involving a fabricated alibi, ‘fabrication of evidence of innocence is cogent evidence of guilt.’ ” Kellensworth v. State, 276 Ark. 127, 633 S.W.2d 21, 23-24 (1982), quoting Harvey v. United States, 215 F.2d 330, 332 (D.C.Cir.1954).

The state introduced two videotapes showing statements that Mr. Martin gave to the police in Lawton, Oklahoma. In those statements, Mr. Martin said that around 1:00 a.m. or 2:00 a.m. on the morning of October 12, 1991, he was at a club in Lawton with Mr. Henry; he also told the police that he never went to Arkansas on the weekend in question. He said instead that he and Mr. Henry left for Tulsa about 7:00 a.m. or 8:00 a.m. that morning but stopped partway and turned around because of difficulty with the ear’s brakes. He confirmed that Mr. Henry got a ticket for speeding. He stated that they got back to Lawton about 1:30 p.m. or 2:30 p.m.

Mr. Martin put on one witness in his defense, a staff sergeant who served with him in the military. The sergeant testified that on October 12, 1991, he left his own house in Lawton, Oklahoma, about noon, washed his car for about half an hour, and then went to Mr. Martin’s house. He stated that he and Mr. Martin were together from then until about 2:30 p.m., when Mr. Henry drove up in Mr. Martin’s car, and that there was another person in the car with Mr. Henry. The sergeant acknowledged that although he read about Mr. Martin’s subsequent arrest for a kidnapping and murder that had allegedly taken place on the morning of the day that he and Mr. Martin were together in the afternoon, he never contacted the police in Little Rock.

After considering all of the evidence offered to corroborate Mr. Henry’s testimony, we have no difficulty concluding that a reasonable jury could find from it that Felicia Martin was kidnapped and murdered — her unexplained disappearance from work, having left personal items and her car at her workplace; the discovery of her glasses, without which she had said she could not see, at a curb behind her workplace; and her death by strangulation after a struggle. Nor do we have any hesitation about concluding that a reasonable jury could find that the corroborating evidence tended to connect Mr. Martin with that crime — the sighting of his gold Cadillac at the college around the time that Mrs. Martin arrived for work; Mrs. Martin’s being seen beside the ear; the contemporaneous disappearance of both Mrs. Martin and the car; the discovery in Mr. Martin’s ear of a chain whose pattern was consistent with the abrasions on Mrs. Martin’s neck; the similarity between the tire tread marks where Mrs. Martin’s body was found and those on Mr. Martin’s car; and the ticketing of Mr. Martin’s car during a period for which he offered conflicting explanations of his whereabouts (returning from Tulsa at noon with Mr. Henry, subsequently arriving in Lawton at 1:30 p.m. or 2:30 p.m., according to his statements to the police; or at home alone and with his staff sergeant between 12:30 p.m. and 2:30 p.m., according to the sergeant). The corroborating evidence thus “independently establish[ed] the crime and tend[ed] to connect the accused with its commission.” Sanders v. State, 310 Ark. 510, 838 S.W.2d 359, 360 (1992). That evidence was also strong enough, in our view, to raise more than “a suspicion of guilt.” Henderson, 652 S.W.2d at 19.

*217 We hold, then, that the corroborating evidence was substantial enough as a matter of law to support the jury’s implicit finding that Mr. Henry’s testimony was truthful. Under these circumstances, we do not believe that there is any “reasonable probability,” Strickland v. Washington, 466 U.S. 668, 694, 104 S.Ct. 2052, 2068, 80 L.Ed.2d 674 (1984), that if the state appeals court had considered the merits of Mr. Martin’s claim of insufficient evidence, the appeals court would have reversed the state trial court’s denial of Mr. Martin’s lawyer’s motion for a directed verdict. We therefore hold that Mr. Martin suffered no prejudice as a result of his state trial lawyer’s actions in that regard.

III.

Mr. Martin argues that the state trial court’s refusal to instruct the jury on the lesser included offense of second-degree murder violated his due process rights. See, e.g., Henderson v. Kibbe, 431 U.S. 145, 154, 97 S.Ct. 1730, 1736-37, 52 L.Ed.2d 203 (1977). Although Mr. Martin’s premise is not completely clear from his appellate brief, we believe that he may be contending that the state trial court, and the state appeals court, incorrectly interpreted Arkansas law on when a jury instruction is required on a lesser included offense. In that regard, we observe that a state court’s error in interpreting state law does not ordinarily give rise to a constitutional claim justifying habeas relief. See, e.g., Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 479-80, 116 L.Ed.2d 385 (1991); see also Anderson v. Goeke, 44 F.3d 675, 681 (8th Cir.1995), and Schleeper v. Groose, 36 F.3d 735, 737 (8th Cir.1994).

To the extent that Mr. Martin may be asserting that the Arkansas law itself is a violation of his due process rights under the Constitution, we do not believe, given the state of the evidence contained in this record, that the state trial court’s refusal to instruct the jury on second-degree murder was “a fundamental defect resulting in a complete miscarriage of justice.” Baker v. Leapley, 965 F.2d 657, 659 (8th Cir.1992) (per curiam); see also Closs v. Leapley, 18 F.3d 574, 579 (8th Cir.1994), and Frey v. Leapley, 931 F.2d 1253, 1255 (8th Cir.1991). We therefore reject Mr. Martin’s arguments in that respect.

IV.

For the reasons stated, we affirm the judgment of the district court.

Notes

. The Honorable Stephen M. Reasoner, Chief Judge, United States District Court for the Eastern District of Arkansas, adopting the report and recommendation of the Honorable H. David Young, United States Magistrate Judge for the Eastern District of Arkansas. See 28 U.S.C. § 636(b)(1)(B).