Ohio Rev. Code § 311.15
When the term of office for which a sheriff has been elected expires, or he resigns or moves outside the county, such sheriff shall deliver all writs of execution and all other processes, of whatever description, whether executed or not, and all goods and chattels taken by him, in execution or on attachment, which remain in his hands, together with all bonds, to the person elected or appointed and qualified to discharge the duties of sheriff, and he shall make the necessary and proper return upon each such writ or other process so far as executed. Such sheriff shall also deliver to his successor all prisoners in the county jail or otherwise in his custody, with all bail bonds taken by him and remaining in his possession. The new sheriff shall receive all such prisoners, writs, or other processes, and he shall execute such writs and processes as remain unexecuted in whole or in part as if they had been directed to him originally. No process shall be directed to or executed by a sheriff whose term of office has expired.
R.C. §311.15