Ohio Revised Code Title XXIX. Crimes Procedure § 2949.21

A writ for the execution of the death penalty shall be directed to the sheriff by the court issuing it, and the sheriff, within thirty days and in a private manner, shall convey the prisoner to the facility designated by the director of rehabilitation and correction for the reception of the prisoner. For conducting the prisoner to the facility, the sheriff shall receive like fees and mileage as in other cases, when approved by the warden of the facility. After the procedures performed at the reception facility are completed, the prisoner shall be assigned to an appropriate correctional institution, conveyed to the institution, and kept within the institution until the execution of his sentence.