Massachusetts General Laws Part I. Administration of the Government (Ch. 1-182) Ch. 53, § 62

If a person nominated to be voted for at a city or town primary dies before the day of the primary, or withdraws his name from nomination, or is found ineligible, and there is no other candidate for the party nomination for the office, the vacancy may be filled by vote of the town committee in a town, by vote of the city committee if it occurs for an office to be filled by all the voters of a city, or by vote of the ward committee if it occurs for an office to be filled by the voters of a ward. In cases of vacancies caused by withdrawal, nominations to fill such vacancies shall be filed with the town clerk within twenty-four week-day hours, by a certificate signed by the chairman and secretary of said committee, or if the vacancy occurs in a city, with the city clerk within forty-eight week-day hours, by a similar certificate, signed by the chairman and secretary of the city committee or of the ward committee, as the case may be. No vacancy caused by withdrawal shall be filled before the withdrawal has been filed. If there is a failure to make a nomination at a city or town primary by reason of a tie vote, the vacancy, if in respect to an office to be filled by all the voters of the city or town, shall be filled by vote of the city or town committee and, if in respect to an office to be filled by the voters of a ward, by vote of the ward committee; provided, that any such vacancy shall be filled only by the choice of one of the candidates receiving the tie vote.