Ohio Revised Code Title I. State Government § 113.19

(A) When the term of the treasurer of state or acting treasurer of state expires, or he resigns, is removed, or is suspended from office, an audit shall be made by the auditor of state of the state treasury and the custodial funds of the treasurer of state.  The liability of the outgoing treasurer of state, acting treasurer of state, or their respective sureties, shall not be discharged until the audit is completed by the auditor of state.

(B) Upon the expiration of the term of office of the treasurer of state or in the event of a vacancy in the office of treasurer of state by reason of death, resignation, removal or suspension from office, or otherwise, the treasurer or his legal representative shall transfer and deliver to his successor all documents evidencing a deposit or investment held by him.  For the investments and deposits so transferred and delivered, the treasurer of state shall be credited with and his successor shall be charged with the amount of money held in such investments and deposits.