Ohio Rev. Code § 5553.09
If the board of county commissioners is of the opinion that the proposed improvement is of sufficient importance to the public to cause the compensation and damages on account thereof to be paid to the persons entitled thereto out of the county treasury, it may so order If the board is of the opinion that such improvement is not of sufficient importance to cause the compensation and damages to be paid from the treasury, it may determine to proceed with the improvement only upon the condition that the compensation and damages, or such part thereof as it deems reasonable and just, be paid by the landowners of lands within the vicinity who will be benefited by the improvement, and the balance shall be paid out of the treasury. In such event the board shall include in its order a schedule setting forth the names of such landowners, a pertinent description of such lands, and a statement of the amount of compensation and damages to be paid by the owner of each parcel of such lands. When a portion of the compensation and damages is ordered to be paid by the landowners who will be benefited by the improvement, the board may abandon the improvement on the failure of such benefited landowners to pay the compensation and damages adjudged against them by the time fixed therefor.
R.C. §5553.09