At the conclusion of each criminal case the court shall tax the costs against the party responsible for payment and shall cause to be delivered to such responsible party a complete statement of the costs, specifying each item of service and the fee assessed for such service. When the costs are ordered paid by the county, the statement of costs shall not include that portion of the docket fee which is to be paid to the county general fund for the services of the clerk of the district court and the sheriff. Such statement shall be filed in the office of county clerk and shall be allowed by the board of county commissioners and paid as other claims against the county. When the claim has been allowed by the board of county commissioners, payment shall be made to the clerk of the court who shall distribute such funds to the persons entitled to receive them.