Ohio Rev. Code § 2335.33: Costs collected by sheriffs.

Each sheriff shall pay to the clerk of the court of common pleas all costs collected by such sheriff or his deputies, except when collected upon process from the supreme court, the probate court, or from the court of common pleas of another county in which cases the sheriff shall pay such costs to the clerk of the court from which the process issued. A sheriff may pay costs to the parties entitled thereto.