Ohio Rev. Code § 5521.03
Where the board of county commissioners, under authority of section 5521.02 of the Revised Code, co-operate with the director of transportation in any work within a municipal corporation, such board and the legislative authority of the municipal corporation may co-operate with respect to such work, and the legislative authority of the municipal corporation may assume and pay such portion of that part of the entire cost assumed in the first instance by the board as may be agreed upon between council and the board. In such event all of the proceedings involving such co-operation between the board and the municipal corporation shall be conducted under sections 5557.01 to 5557.08 of the Revised Code. The municipal corporation shall have the same authority to make special assessments, levy taxes, and issue and sell notes and bonds for the purpose of meeting that portion of the cost assumed by it, as is or may be granted to it with respect to improvements of the same character constructed under its exclusive jurisdiction and control. The municipal corporation shall, prior to the making by the board of the contract provided for by section 5521.05 of the Revised Code, provide and pay that portion of the cost assumed by it into the county treasury, to the credit of a special fund which shall be created for the construction of the improvement. The contract and certificate required of the board by section 5521.05 of the Revised Code shall embrace the funds furnished by the municipal corporation, which funds shall be disbursed upon the requisition of the director.
R.C. §5521.03