The local party rules, governing a political party in any municipality, may be amended by one of the three following methods:
(1) By a caucus of its enrolled party members, (2) by a convention of delegates chosen by its enrolled party members in a manner prescribed in such rules or (3) by its town committee. Whenever, in any municipality, the method of amending the local party rules of a party is by the town committee, such rules may also be amended either by a caucus of its enrolled party members or by a convention of delegates chosen by its enrolled party members in a manner prescribed in such rules, whichever such rules specify, which caucus or convention, as the case may be, shall forthwith be called by the chairman of its town committee upon the filing with the registrar of voters of such party in such municipality of a petition signed by at least five per cent or five hundred, whichever is less, of its enrolled party members in such municipality, and such caucus or convention, as the case may be, shall be held within a period of time reasonably necessary to convene the same, which period of time shall be prescribed in its rules. Whenever the method of amendment prescribed in accordance with the provisions of this section for a party in any municipality consists of or involves a convention of delegates chosen by its enrolled party members under its party rules, such rule or amendment so prescribing such method of amendment shall also prescribe the manner in which such delegates are to be chosen.(1957, P.A. 518, S. 40; 1958 Rev., S. 9-70; 1963, P.A. 17, S. 4.)