Ohio Rev. Code Ann. § 307.50

When any person charged with a felony has fled to any other state, territory, or country, and the governor has issued a requisition for such person or requested the president of the United States to issue extradition papers, or the prosecuting attorney of any county in the state seeking the return of a felon has received notice of waiver of extradition, the board of county commissioners may pay, from the county treasury to the agent designated in such requisition, request to the president, or order by the prosecuting attorney seeking return, all necessary expenses of pursuing and returning the person so charged, or so much of such expenses as seem just.