Ohio Rev. Code § 6131.34
If the appellants, on claims for compensation or damages, do not recover a judgment for more than the amount of compensation or damages awarded by the board of county commissioners, the costs on the hearing as to compensation or damages on appeal shall be taxed against the appellants. If the amount recovered is greater than the amount awarded by the board, the costs shall be taxed against the county.
The prosecuting attorney shall represent the county in all appeals on questions of compensation or damages. On appeals of other matters which are tried to the court sitting as a court of equity, the court shall adjudge the costs as it deems just and equitable except as otherwise provided in section 6131.01 to 6131.64, inclusive, of the Revised Code.
R.C. § 6131.34