Ohio Rev. Code § 6135.23
When the board of county commissioners finds on file with the clerk of the board of county commissioners a petition praying for the location or improvement of a ditch, drain, or watercourse in such county, the waters from which flow into or through an adjoining county in another state, and it is of the opinion that the outlet for such proposed improvement is insufficient, it may enter into an agreement with the proper officials of such adjoining county for the construction or improvement of the outlet for such ditch, drain, or watercourse by such lower county and for the payment by such upper county to the lower county of a sum of money agreed upon, between said board and the proper officials of the lower county, for the construction or improvement of such outlet. Such sum shall be payable into the treasury of such lower county upon the completion of the improvement of the outlet as agreed upon.
The board of the upper county shall assess upon the lots and lands, public corporations, the state of Ohio, and public or corporate roads or railroads in such county, benefited by the improvement, the costs of the location and construction thereof in the county, with the sum of money agreed to be paid to the lower county for the improvement of the outlet therefor.
R.C. § 6135.23