(a) The Director of Public Health and Welfare shall provide the Clerk of the criminal branch of the Municipal Court with a statement, on the first day of every month, showing in detail the collection for the previous month of all cash fines imposed on prisoners sentenced to the House of Correction by the Court. In any case where money is not collected, but the money fine imposed, or any portion of it, is worked out by the prisoner or is by proper authority remitted, he or she shall so report the same in the statement rendered.
(b) The Clerk of the criminal branch of the Municipal Court shall enter upon the dockets of the judges of such Court, in the proper respective places, the collections and dispositions of money, fined according to the statement rendered by the Director of Public Health and Welfare.