Constitution of the State of Ohio Art. III, § 17

When a vacancy occurs in both the office of governor and lieutenant governor because of the death, conviction on impeachment, resignation, or removal of the persons elected to those offices prior to the expiration of the first twenty months of a term, a governor and lieutenant governor shall be elected at the next general election occurring in an even-numbered year after the vacancy occurs, for the unexpired portion of the term.  The officer next in line of succession to the office of governor shall serve as governor from the occurrence of the vacancy until the newly elected governor has qualified.

If by reason of death, resignation, or disqualification, the governor-elect is unable to assume the office of governor at the commencement of the gubernatorial term, the lieutenant governor-elect shall assume the office of governor for the full term.  If at the commencement of such term, the governor-elect fails to assume the office by reason of disability, the lieutenant governor-elect shall serve as governor until the disability of the governor-elect terminates.