Ohio Rev. Code Ann. § 705.81

If the mayor is temporarily absent from the municipal corporation, or becomes temporarily disabled by sickness, accident, or for any other cause, the heads of the departments shall, during the absence or disability, perform the duties of the mayor under the designation of acting mayor, in the following order: village solicitor or city director of law, director of public service, director of public safety, auditor, and treasurer. If the mayor dies or removes his residence from the municipal corporation during the term of his office, the succession to the office of mayor shall be from the heads of the departments in the order provided in this section, and the successor shall become the mayor of the municipal corporation for the unexpired term. In the event of any temporary disability or absence on the part of any director or department head, the mayor may, in writing, designate some suitable person to perform his duties until he resumes his office.