Ohio Rev. Code Ann. § 3327.11

A board of education in a district which does not maintain a high school and which pays the tuition of a school resident of the district in a high school in another district, or a board which pays the tuition of a school resident of the district, in a high school in another district, of higher grade than that maintained in the given district may furnish the cost of such child's room and board while attending such school or a part of such cost, provided such amount is less than the cost of transportation of such child and provided such action is approved by the county board.