Ohio Rev. Code § 1901.23
Writs and process in a municipal court shall be served, returned, and publication made in the manner provided for service, return, and publication of summons, writs, and process in the court of common pleas.
In any civil action or proceeding in which the subject matter of the action or proceeding is located within the territory or a defendant resides or is served with summons within the territory, the court may issue summons, orders of interpleader, all other writs, and mesne and final process, including executions necessary or proper for the complete adjudication of the issues and determination of the action, to the bailiff for service in the county or counties in which the court is situated and to the sheriff of any other county against one or more of the remaining defendants.
All warrants, executions, subpoenas, writs, and processes in all criminal and quasi-criminal cases may be issued to the bailiff of the court, a police officer of the appropriate municipal corporation, or to the sheriff of the appropriate county.
In any civil action in which the bailiff is a party or is interested, writs and process shall be directed to the sheriff. If both of these officers are interested, the writs and process shall be directed to and executed by a person appointed by the court or a judge of the court, and that person has the same power to execute the writs and process that the bailiff has. The return of the appointee shall be verified by affidavit, and he is entitled to the fees allowed to the bailiff for similar service.
R.C. § 1901.23