(a) The city manager shall provide for the appointment of a clerk of the municipal courts of record, who shall be known as the municipal clerk. The municipal clerk shall perform, as applicable, the duties prescribed by law for the county clerk of a county court at law. In addition, the clerk shall:
(1) maintain central docket records for all cases filed in the municipal courts of record; and
(2) maintain an index of all municipal court of record judgments in the same manner as county clerks are required by law to prepare for criminal cases arising in county courts.
(b) The governing body of the city shall provide the courts with other municipal court personnel that the governing body determines necessary for the proper operation of the courts. Those persons shall perform their duties under the direction and control of the clerk or the municipal judge to whom assigned. The governing body shall determine the salaries of the court personnel.