Ohio Rev. Code § 5139.22: Transportation costs.

Each county shall bear all of the expenses incident to the transportation of a child committed to the department of youth services by the juvenile court of that county from that county to the institution to which the department has assigned the child and shall bear the fees and costs allowed in similar cases. The fees, costs, and expenses shall be paid from the county treasury upon itemized vouchers certified to by the judge of the juvenile court.