Ohio Revised Code Title III. Counties § 307.49

The board of county commissioners may offer such rewards as the nature of the case requires, for the detection or apprehension of any person charged with or convicted of felony, and on the conviction of such person, pay it from the county treasury, together with all other necessary expenses, not otherwise provided for by law, incurred in making such detection or apprehension. The board may, on the collection of a recognizance given and forfeited by such person, pay the reward so offered, or any part thereof, together with all other necessary expenses so incurred and not otherwise provided for by law.