Section 14B. In cities and towns in which the duty of listing residents for the purposes of determining their right to vote is performed by officers other than registrars or assistant registrars, the provisions of this chapter relative to registrars and assistant registrars shall apply to such officers when performing like duties in such cities and towns, except as otherwise expressly provided in any special law or in this section. Where in any special law April first is stated as the date as of which the legal residence of any person shall be determined, such residence shall be determined as of January first instead of April first, and if any provision of this chapter contains a date for the performance of an official act by a board of registrars, registrar or assistant registrar, and by special law a different date is fixed for the performance of such act in any city or town by the same or any other board or officer, the earlier of such dates shall in such city or town prevail over the later date.