Ohio Rev. Code § 313.04
When the coroner is absent temporarily from the county, or when on duty with the armed services of the United States, the state militia, or the American red cross, or when unable to discharge the duties of the office of coroner, such coroner may appoint a person with the necessary qualifications to act as coroner during such absence, service, or disability.
When there is a vacancy in the coroner's office as a result of death or resignation and the vacancy cannot be filled by election or appointment as provided in section 305.02 of the Revised Code, or if no one runs for the office of coroner and, for that reason, the office is vacant, the board of county commissioners may contract with another county's coroner to exercise the powers and perform the acts, duties, or functions of the coroner. In addition to the applicable amounts of compensation specified in sections 325.15 and 325.18 of the Revised Code, the coroner with whom the board contracts may receive a supplemental payment for services rendered. The duration of the contract shall not extend beyond the last day of the term for which there was a vacancy.
R.C. § 313.04