Ohio Rev. Code § 5561.12: Cost of repairs.

After the completion of construction work, grade crossings and approaches shall be kept in repair as follows:

(A) When the public way crosses a railroad or interurban railway, by an overhead bridge, the cost of maintenance must be borne by the county or state, as may be provided by law.

(B) When the public way passes under a railroad or interurban railway, the bridge and its abutments shall be kept and maintained by the railroad or interurban railway company in such proportions as are fixed by agreement between the parties, or, in the absence of such agreement, in such proportions as are fixed by the court of common pleas of the county in which the improvement is located, and the public way and its approaches shall be maintained and kept in repair by the county in which they are situated or by the state.