Ohio Rev. Code § 341.12
In a county not having a sufficient jail or staff, the sheriff shall convey any person charged with the commission of an offense, sentenced to imprisonment in the county jail, or in custody upon civil process to a jail in any county the sheriff considers most convenient and secure. As used in this paragraph, any county includes a contiguous county in an adjoining state.
The sheriff may call such aid as is necessary in guarding, transporting, or returning such person. Whoever neglects or refuses to render such aid, when so called upon, shall forfeit and pay the sum of ten dollars, to be recovered by an action in the name and for the use of the county.
Such sheriff and the sheriff's assistants shall receive such compensation for their services as the county auditor of the county from which such person was removed considers reasonable. The compensation shall be paid from the county treasury on the warrant of the auditor.
The receiving sheriff shall not, pursuant to this section, convey the person received to any county other than the one from which the person was removed.
R.C. § 341.12