Rule 45(B), Ohio Rules of Civil Procedure:
A subpoena may be served by a sheriff, bailiff, coroner, clerk of court, constable, or a deputy of any, by an attorney at law, or by any other person designated by order of court who is not a party and is not less than eighteen years of age. Service of a subpoena upon a person named therein shall be made by delivering a copy of the subpoena to the person, by reading it to him or her in person, by leaving it at the person's usual place of residence, or by placing a sealed envelope containing the subpoena in the United States mail as certified or express mail return receipt requested with instructions to the delivering postal authority to show to whom delivered, date of delivery and address where delivered, and by tendering to the person upon demand the fees for one day's attendance and the mileage allowed by law. The person responsible for serving the subpoena shall file a return of the subpoena with the clerk. When the subpoena is served by mail delivery, the person filing the return shall attach the signed receipt to the return. If the witness being subpoenaed resides outside the county in which the court is located, the fees for one day's attendance and mileage shall be tendered without demand. The return may be forwarded through the postal service or otherwise.
Rule 17(D), Ohio Rules of Criminal Procedure:
A subpoena may be served by a sheriff, bailiff, coroner, clerk of court, constable, marshal, or a deputy of any, by a municipal or township policeman, by an attorney at law or by any person designated by order of the court who is not a party and is not less than eighteen years of age. Service of a subpoena upon a person named therein shall be made by delivering a copy thereof to such person or by reading it to him in person or by leaving it at his usual place of residence, and by tendering to him upon demand the fees for one day's attendance and the mileage allowed by law. The person serving the subpoena shall file a return thereof with the clerk. If the witness being subpoenaed resides outside the county in which the court is located, the fees for one day's attendance and mileage shall be tendered without demand. The return may be forwarded through the postal service, or otherwise.