Ohio Rev. Code § 5521.07
In all cases in which the director of transportation desires to cooperate with the board of county commissioners or with any municipal corporation in the establishment, construction, reconstruction, widening, maintenance, repair, railway grade crossing elimination, or other improvement of any section or portion of a state highway, the director may, as a condition precedent to his extending such cooperation, require such county or municipal corporation to provide the portion of the cost of such improvement which it proposes to furnish, and to pay the cost into the state treasury to the credit of the highway operating fund. Such requirement may be prescribed by the director at any time after the board or legislative authority of the municipal corporation has, by resolution, proposed such cooperation, and when such requirement is prescribed, the director may not proceed with the improvement upon the cooperative basis proposed until such requirement is met.
R.C. §5521.07