Ohio Revised Code Title III. Counties § 341.141

(A) The sheriff of a county in this state shall not transfer a prisoner to a contiguous county in an adjoining state as provided in section 341.12 of the Revised Code unless there is deposited weekly with the sheriff of the contiguous county an amount equal to the actual cost of keeping and feeding each prisoner committed to the custody of that sheriff for the use of the jail of that county, and the same amount for a period of time less than one week.  If a prisoner is discharged before the expiration of a week for which the cost of keeping and feeding the prisoner has been deposited, the excess of the amount shall be refunded.

(B) The minimum standards for jails that are applicable for jails in the adjoining state shall apply to a jail in that adjoining state that receives prisoners as provided in section 341.13 of the Revised Code.

(C) All other terms of the transfer of a prisoner from a county in this state to a contiguous county in an adjoining state shall be as agreed upon by the board of county commissioners, any applicable governmental entity in the receiving county, and the sheriffs involved in the transfer.

(D) If a prisoner is transferred to a contiguous county of an adjoining state as provided in section 341.12 of the Revised Code, jurisdiction over the transferred prisoner shall remain with the Ohio governmental agencies and entities that would have jurisdiction over the prisoner if the prisoner had not been so transferred, including the Ohio court to which the prisoner's case is assigned.