Ohio Rev. Code Ann. § 5149.38
(A) In each target county and in each voluntary county, subject to division (B) of this section and not later than thirty days after the effective date of this section , a county commissioner representing the board of county commissioners of the county, the administrative judge of the general division of the court of common pleas of the county, the sheriff of the county, and an official from any municipality operating a local correctional facility in the county to which courts of the county sentence offenders shall agree to, sign, and submit to the department of rehabilitation and correction for its approval a memorandum of understanding that does both of the following:
(F)
(1) In each county, the sheriff shall determine the per diem costs for local correctional facilities in the county for the housing of prisoners who serve a term in the facility pursuant to division (B)(3)(c) of section 2929.34 of the Revised Code, as follows:
(G) As used in this section: