Ohio Rev. Code § 2949.20: Costs in case of final judgment of reversal.

In any case of final judgment of reversal as provided in section 2953.07 of the Revised Code, whenever the state of Ohio is the appellee, the clerk of the court of common pleas of the county in which sentence was imposed shall certify the case to the state public defender for reimbursement in the report required by section 2949.19 of the Revised Code, subject to division (B) of section 2949.19 of the Revised Code.