Mo. Rev. Stat. § 550.240
In all criminal cases which have been finally determined before an associate circuit judge in which the county shall be liable for any costs incurred therein, the clerk responsible for collecting fees in cases determined by such judge shall certify a complete itemized fee bill thereof to the county commission for payment, which fee bill shall be examined and audited by the prosecuting attorney and the judge. Whenever the state shall be liable under any law for costs incurred in any examination of a felony before any associate circuit judge, or in any misdemeanor case which is not finally determined before an associate circuit judge, the clerk serving such judge shall calculate, certify and return to the clerk of the circuit court of the county a complete statement of costs, specifying each item of service and the fee therefor, together with all the papers and docket entries in the case. The clerk of the circuit court shall thereupon make out a fee bill of all such costs which are legally chargeable against the state or county, which shall be examined by the prosecuting attorney. The circuit clerk shall prepare a bill against the state containing only costs which are payable to the county. All such fee bills shall thereafter be proceeded with in all respects as in the case of fee bills for costs incurred in cases before circuit judges.
§ 550.240, RSMo