A filing fee of one hundred dollars ($100) shall be required with every petition to appoint a private judge. This one hundred dollar ($100) fee shall be distributed in equal parts to the Administrative Office of Courts and to the office of the clerk of the county in which the case being heard by the private judge is pending. Otherwise, costs in an action brought before a private judge shall be taxed and distributed in the same manner as costs in the circuit court of the county in which the case is filed.