Ohio Rev. Code Ann. § 2311.40

In all civil actions in which the venue is changed, the clerk of the county to which such action has been sent, upon its termination in the courts of his county, shall make a full itemized bill of all costs and expenses of such action which have been paid out of the county treasury of the county to which it was changed, and certify such bill of costs and expenses to the county auditor of the county from which such action was sent. The auditor of the county in which it was instituted shall draw his warrant upon the treasury of his county, payable to the treasurer of the county, in which such trial was conducted for the full amount of costs and expenses, certified as provided in this section.