King, C. J.

This appeal involves an application, duly served on the defendant, for an order under General Statutes § 52-410 to compel arbitration under the uninsured motorist provisions in Part IV of an automobile insurance policy issued by the defendant to Page and Doris Porter, husband and wife, covering the operation of their Corvair automobile.

The plaintiff, Sarah Frager, was operating the insured automobile with the permission of its own *272 ers when it ran off the left side of the road and collided with a utility pole, resulting in injury to the plaintiff. The plaintiff alleged in her application that this accident occurred because the Corvair was struck by an oncoming automobile which did not stop and the owner and operator of which remain unidentified. The defendant, inter alia, denied that the Corvair had been in contact with another vehicle. This question of contact is, under the terms of the policy as hereinafter pointed out, a decisive issue in this appeal.

The only portion of the policy directly involved in this appeal is entitled “Part IV — Protection Against Uninsured Motorists”, and in this part the insurer contracted to pay all sums which an insured person shall be legally entitled to recover, as damages for certain bodily injuries, from the owner or operator of an “uninsured automobile”. 1 See, generally, note, 79 A.L.R.2d 1252; 6 Later Case Service 368 and current pocket supplement. The policy definition of “uninsured automobile” includes “a hit-and-run automobile”, which in turn is defined as “an automobile which causes bodily injury to an insured arising out of physical contact of such automobile with the insured or with an automobile which the insured is occupying at the time of the accident, provided: . . . there cannot be ascertained *273 the identity of either the operator or the owner of such ‘hit-and-run automobile’ ”. Thus, an automobile may be a hit-and-run automobile, and consequently an uninsured automobile within the policy definition of that term, if, but only if, it makes physical contact with an insured claimant or with an automobile in which an insured claimant is an occupant.* 2

The trial court concluded that the question whether there was contact between the vehicle operated by the plaintiff and the unidentified vehicle, as she claimed, so as to make that other vehicle a “hit-and-run” vehicle and so an “uninsured automobile” under the terms of the policy was a matter to be determined by arbitration. 3 The defendant appealed.

While the defendant, in its answer, specially denied each of the material allegations of the plaintiff’s application, apparently improperly and in violation of ■§§ 73, 116, 117 and 118 of the Practice Book, on this appeal it is conceded that the plaintiff is an insured party under the policy and that *274 the only issue is whether the question of contact should be resolved, as the plaintiff claims, by the arbitrators or, as the defendant claims, by the trial court. The answer to this question depends upon the proper interpretation of the terms relating to arbitration as set forth in Part IY of the policy.

The duty to arbitrate may be created by contract. But a party cannot be compelled to arbitrate a dispute unless he has contracted so to do. Ginsberg v. Coating Products, Inc., 152 Conn. 592, 596, 210 A.2d 667, and cases cited; cf. International Union v. General Electric Co., 148 Conn. 693, 700, 174 A.2d 298. A party who has contracted to arbitrate certain matters has no obligation to arbitrate any matters other than those he has agreed to arbitrate. Batter Building Materials Co. v. Kirschner, 142 Conn. 1, 5, 110 A.2d 464. Whether a particular dispute is arbitrable is a question for the court, unless, by appropriate language, the parties have agreed to arbitrate that question, also. Connecticut Union of Telephone Workers, Inc. v. Southern New England Telephone Co., 148 Conn. 192, 198, 169 A.2d 646; College Plaza, Inc. v. Harlaco, Inc., 152 Conn. 707, 206 A.2d 832.

The clause in the policy now under consideration which constitutes the agreement to arbitrate, and which, necessarily, determines what issues are to be submitted to arbitration, appears in Part IY under the subtitle “Arbitration” and provides as follows: “If any person making claim hereunder and the company do not agree that such person is legally entitled to recover damages from the owner or operator of an uninsured automobile because of bodily injury to the insured, or do not agree as to the amount of payment which may be owing under this Part, then, upon written demand of either, the *275 matter or matters upon which such person and the company do not agree shall be settled by arbitration . . . and judgment upon the award rendered by the arbitrators may be entered. . . . Such person and the company each agree to ... be bound by any award made by the arbitrators pursuant to this Part.”

This agreement for arbitration is not a broad, all-encompassing provision of the types found in Gores v. Rosenthal, 150 Conn. 554, 555, 192 A.2d 210, and College Plaza, Inc. v. Harlaco, Inc., 152 Conn. 707, 206 A.2d 832, and cases cited. The provision applies only to a claim under Part IV of the policy as to an uninsured motorist. Unless the claim relates to an uninsured motorist, the arbitration provision is inapplicable. Under this provision, the only issues to be arbitrated are: (1) the insured’s right to recover damages from the owner or operator of an uninsured automobile, and (2) the amount of such damages. Hartford Accident & Indemnity Co. v. Travelers Ins. Co., 25 Conn. Sup. 414, 417, 206 A.2d 847; Matter of Motor Vehicle Accident Indemnification Corporation (Downey), 11 N.Y.2d 995, 183 N.E.2d 758; Matter of Rosenbaum (American Surety Co. of New York), 11 N.Y.2d 310, 313, 183 N.E.2d 667; Murtaugh v. American States Ins. Co., 25 Ohio Op. 2d 106, 107, 187 N.E.2d 518; Cruger v. Allstate Ins. Co., 162 So. 2d 690, 693 (Fla.).

It is not the right to recover damages from the defendant insurance company which is made arbi-trable but the right to recover damages from the uninsured motorist. If the arbitrators find this issue in favor of the plaintiff, then they determine the amount of those damages, and it is that amount which the defendant has contracted to pay under Part IV of its policy. The words “matter or matters *276 upon which snch person and the company do not agree” in the arbitration clause clearly refer to the two issues previously mentioned in that clause, namely, the right to recover damages from the owner or operator of an “uninsured automobile” and the amount of such damages.

That the unidentified vehicle was an “uninsured automobile” is a condition precedent to the applicability of Part IV of the policy which includes the arbitration provision. The policy does not provide generally for arbitration of disputes between the plaintiff and the defenddnt but provides only for arbitration of the foregoing two issues involving an “uninsured automobile”, which, as previously noted, includes, in certain cases, a “hit-and-run” automobile. Whether an unidentified automobile is an “uninsured automobile” within the terms of the policy is a question independent of whether the plaintiff would be legally entitled to recover damages from the owner or operator thereof if he could have been identified and sued. Murov v. Lumber-mens Mutual Casualty Co., 25 Conn. Sup. 504, 507, 209 A.2d 517. The former question pertains to coverage under Part IV of the policy. Cruger v. Allstate Ins. Co., supra. The latter concerns liability of the owner or operator of the uninsured car.

The defendant’s liability to the plaintiff is dependent upon coverage under the policy, as well as on the plaintiff’s legal right to damages from an uninsured motorist. And coverage depends not only on the terms of the policy but also on whether the facts of a particular accident bring it within that coverage. Part IV of this policy, when construed as a whole and in accordance with settled principles of contract law, contains no provision *277 that coverage of a particular accident is an arbi-trable question.

The plaintiff claims that the two issues of (1) liability of the uninsured motorist and (2) coverage are inseparably intermeshed and that, in order fully to carry out the agreement to arbitrate the first, the parties must arbitrate the second also. We do not agree. In this particular case, the answer to the question of contact is determinative of the question of coverage. It is not, however, determinative of the question of the legal liability of the owner or operator of the unidentified vehicle. That question might exist even though the plaintiff had succeeded in avoiding actual contact with that vehicle. But in such a situation there would be no coverage under the defendant’s policy.

We need not now determine whether a judicial finding that there was contact would be binding upon the arbitrators. At most, it would be but one element in the arbitrable issue of liability of the hit-and-run motorist. Such a finding, however, would not prejudice the plaintiff’s case before the arbitrators, and might be likely to enhance it. Thus, a judicial determination that there had been contact, although included in the nonarbitrable issue of coverage, would not impinge upon the arbitrators’ freedom to determine for themselves the issues committed to them, which are (1) the liability of the owner or operator of the unidentified automobile and (2) the amount of damages flowing from that liability.

We cannot extend the scope of the arbitration agreement beyond the fair import of its terms. Since the question of contact was a condition precedent to arbitrability, it should not, itself, have been adjudged to be arbitrable.

*278 Provisions according coverage protection against uninsured motorists are becoming increasingly common, and decisions construing them are appearing with correspondingly increasing frequency. See Public Acts 1967, No. 510; note, 79 A.L.R.2d 1252.

Although there seems to be considerable uniformity in the wording of the material portions of the coverage clauses, there has not been a complete uniformity of decision on the question involved in this appeal. Perhaps the case going farthest in holding arbitrable questions involving coverage in this type of policy is Employers’ Fire Ins. Co. v. Garney, 348 Mass. 627, 631, 205 N.E.2d 8. It is clear from the opinion in that case that the court was influenced by a fear that the courts would be clogged with unwarranted and “piecemeal” litigation.

We do not share this fear. While we are not called upon to determine with finality the precise procedure to be followed, we think the court, as incidental to a properly drawn application to compel arbitration, along the lines utilized in the present case, can adjudicate the question of arbitrability, which would include that of coverage, and that our rule as to pleading in ordinary actions seeking recovery under an insurance policy would apply in such a proceeding. Rochon v. Preferred Accident Ins. Co., 118 Conn. 190, 195, 171 A. 429; Harty v. Eagle Indemnity Co., 108 Conn. 563, 565, 143 A.2d 847. It would appear that, if arbitration is ordered and an award rendered, that award would be enforceable as a judgment, both under the quoted terms of the policy and under §§ 52-417, 52-420 and 52-421 of the General Statutes.

Since the essential allegations in an application to compel arbitration would, except for the determination of the two arbitrable issues, comprise the *279 essential allegations of an ordinary suit for recovery from the defendant under the policy, the amount of the award would in effect be an adjudication of the amount of the defendant’s liability to the plaintiff under the policy and would constitute an amount which the defendant would have no justification for failing to pay.

Under No. 510 of the 1967 Public Acts, previously mentioned, the insurance commissioner is given broad powers of regulation over the terms and conditions of policies providing uninsured motorists coverage. These powers, coupled with the commissioner’s general powers over insurance companies doing business in Connecticut, would appear adequate to protect the public against possible abuses by insurers in connection with claims under provisions for uninsured motorists coverage, whether these abuses were to take the form of involving claimants in unwarranted litigation and procedural complexities or in delaying tactics intended to bring to bear on claimants the compulsive force of economic attrition.

There is error, the judgment is set aside and the case remanded for further proceedings not inconsistent with this opinion.

In this opinion the other judges concurred.

The company agrees “[t]o pay all sums which the insured . . . shall be legally entitled to recover as damages from the owner or operator of an uninsured automobile because of bodily injury . . . sustained by the insured, caused by accident and arising out of the ownership, maintenance or use of such uninsured automobile; provided, for the purposes of this coverage, determination as to whether the insured ... is legally entitled to recover such damages, and if so the amount thereof, shall be made by agreement between the insured . . . and the company or, if they fail to agree, by arbitration.”

The apparent purpose of this requirement is to prevent fraudulent elaims from being made that unidentified automobiles forced claimants’ cars off the road. This purpose is accomplished by requiring visible evidence of the involvement of the claimed hit-and-run automobile. This protection against fraudulent claims obviously works to the disadvantage of an insured claimant who is an occupant of a car which is actually forced to drive off the road in order successfully to avoid a collision with another unidentified automobile.

The memorandum of decision and the finding indicate, and both parties at oral argument agreed, that the court did not itself determine this issue but held that it was an issue to be decided by the arbitrators. This issue, however, is not included in the order to proceed with arbitration set forth in the judgment file. Counsel should cooperate in having the judgment file corrected to reflect accurately the judgment as actually rendered and from which this appeal was taken. Wexler Construction Co. v. Housing Authority, 149 Conn. 602, 607 n.2, 183 A.2d 262.