Ohio Revised Code Title XXIX. Crimes Procedure § 2963.10

A peace officer or other person executing a warrant of arrest issued by the governor, or an agent of the demanding state to whom the prisoner has been delivered, may, when necessary, confine the prisoner in the jail of any county or city through which he may pass.

The officer or agent of a demanding state to whom a prisoner has been delivered following extradition proceedings in another state, or to whom a prisoner has been delivered after waiving extradition in such other state, and who is passing through this state with such a prisoner for the purpose of immediately returning such prisoner to the demanding state may, when necessary, confine the prisoner in the jail of any county or city through which he may pass. Such officer or agent shall produce and show to the keeper of such jail his warrant and other written evidence of the fact that he is actually transporting such prisoner to the demanding state after a requisition by the executive authority of such demanding state. Such prisoner may not demand a new requisition while in this state.

The keeper of such jail must receive and safely keep a prisoner delivered to him under this section, until the officer or agent having charge of him is ready to proceed on his route. Such officer or agent is chargeable with the expense of such keeping.