Ohio Rev. Code Ann. § 753.08

The officer having the execution of the final sentence of a court, magistrate, or mayor shall cause the convicted person to be conveyed to the workhouse as soon as practicable after the sentence is pronounced, and all officers shall be paid the fees therefor allowed by law for similar services in other cases. Such fees shall be paid, when the sentence is by the court, from the county treasury, and when by the magistrate, from the township treasury.