Ohio Rev. Code § 5555.67
Each contract let under section 5555.61 of the Revised Code, shall contain a provision to the effect that if such contract is not completed within the time therein fixed, the county engineer shall, after the expiration of the time fixed for the completion of such contract, keep an accurate account of all expenditures for inspection, supervision, and all other similar engineering services in connection with the improvement, that the contractor shall pay all such expenses incurred in connection with the improvement after the expiration of the time fixed for the completion of such contract, and that the amount of such expenditures shall be retained out of any estimates due or to become due to such contractor. When the engineer allows an estimate to any contractor after the time fixed in the contract for the completion of the improvement, such engineer shall deduct from such estimate any expense for supervision, inspection, or other similar engineering services incurred after the date set for the completion of such contract. The contractor need not pay the cost of such inspection, supervision, and other similar engineering services when the board of county commissioners, for good cause shown, extends the time for the completion of the contract.
R.C. §5555.67