Ohio Revised Code General Provisions § 3.24

Every person holding an elected office under the constitution or laws of this state may administer oaths of office to persons elected or appointed to offices under the constitution or laws of this state if those persons are elected or appointed to offices within the geographical limits of the elected officer's constituency, except that members of the general assembly may administer oaths of office to persons elected or appointed to any office under the constitution or laws of this state.  Nothing in this section shall forbid the judge of a court established by the constitution of this state or a notary public commissioned in this state from administering an oath to any person.

When an oath of office is required to be certified in writing, the person taking the oath shall write the person's signature immediately under the text of the oath.  The person administering the oath under authority of this section shall then write the administering person's signature, the title of the elected office that the administering person holds, and the date;  and shall affix the seal of office if a seal is prescribed for, or has been adopted by, the administering person's office.