Ohio Rev. Code § 2335.16: Taxing of costs by county court judge.

In all causes in which a judge of a county court may fine a person charged with the commission of an offense, such judge shall render judgment for such fine, and shall tax such costs for himself, the constable, and witnesses as are allowed by law.

In any misdemeanor case, all fees due any such officers, if collected, shall be paid into the county treasury, unless the amount of such fees was not taken into account in estimating the allowance to such officer.