§ 328. Option to change to single appointed assessor. In any city or town which has retained the office of elective assessor, the legislative body of such city or town may adopt a local law providing that from and after a date set forth in such local law, which date must be within one year after the date on which such local law was adopted, there shall be but one assessor, to be appointed as provided in section three hundred ten of this title. The legislative body, in its discretion, may determine that a local law adopted pursuant to this section shall be subject to a mandatory or permissive referendum, or not subject to a referendum. Any such referendum shall be conducted in the manner prescribed in section twenty-three or twenty-four of the municipal home rule law, as the case may be. On December thirty-first of the year in which such local law shall take effect, the term or terms of all assessors then in office shall terminate.