Ohio Rev. Code § 5557.03
If any part of the cost of the proposed road improvement is assumed by the municipal corporation, the board of county commissioners, after the approval by it of the surveys, plans, profiles, cross sections, estimates, and specifications, shall cause a copy of the surveys, profiles, and the proposed proportion of cost to be paid by the municipal corporation, to be filed with the legislative authority. The legislative authority shall examine the surveys, profiles, and the proposed proportion of cost to be paid by such municipal corporation. If after such examination the legislative authority is satisfied that the public convenience and welfare require that the improvement be made, it shall, by resolution, so determine, and shall approve the surveys, profiles, and the proposed proportion of cost to be paid by such municipal corporation. After the consent of such legislative authority has been obtained, an agreement shall be entered into by the legislative authority with the board determining what proportion of the cost of such improvement is to be paid by the municipal corporation, which may include the payment of any part of the compensation for land taken and damages to property caused by such improvement, as allowed by the board or fixed as provided by law. All claims for compensation and damages shall be presented to and heard and determined by the board, and all proceedings with reference thereto shall be had by such board in the same manner as though the improvement were located entirely outside a municipal corporation. For the purpose of providing, by taxation, a fund for the payment of the proportion of the cost of the improvement to be paid by the municipal corporation and also the compensation and damages incident thereto, such municipal corporation may levy taxes upon all the taxable property of the municipal corporation, under the same restrictions imposed in the case of taxes levied for the purpose of providing funds for the payment of the municipal corporation's share of the cost of street improvements under the exclusive jurisdiction and control of the legislative authority of a municipal corporation. The legislative authority of the municipal corporation may assess against abutting property owners any part of the proportion of the cost of such improvement, and the compensation and damages to be paid by it. Assessments shall be made in one of the methods provided for in the case of street improvements wholly within the municipal corporation, and under the exclusive control of the legislative authority.
R.C. §5557.03