Ohio Rev. Code Ann. § 3111.14

The court may order reasonable fees for experts and other costs of the action and pretrial proceedings, including genetic tests, to be paid by the parties in proportions and at times determined by the court. The court may order the proportion of any party to be paid by the court, and, before or after payment by any party or the county, may order all or part of the fees and costs to be taxed as costs in the action.