Ohio Rev. Code § 161.03
In the event that the governor, for any of the reasons specified in the constitution, is not able to exercise the powers and discharge the duties of his office, or is unavailable, and in the event the lieutenant governor, president of the senate, and the speaker of the house of representatives are for any of the reasons specified in the constitution not able to exercise the powers and discharge the duties of the office of governor, or are unavailable, the secretary of state, treasurer of state, auditor of state, and attorney general shall, in the order named, if the preceding named officers be unavailable, exercise the powers and discharge the duties of the office of governor until a new governor is elected and qualified, or until a preceding named officer becomes available; provided, that no emergency interim successor to the aforementioned offices may serve as governor.
R.C. § 161.03