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In any city or town where the option to retain elective assessors was exercised in accordance with the provisions of former section fifteen hundred fifty-six of this chapter, the legislative body of such city or town may adopt a local law providing that from and after the first day of January first following the next biennial or general election at which the electors would vote for an assessor, there shall be but one assessor, to be elected at that election. 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.