Mass. Gen. Laws ch. 53 § 101
A person nominated by a nomination paper may, within forty-eight week day hours succeeding five o'clock in the afternoon of the day fixed for opening nomination papers, withdraw his name from nomination by a request signed by him in person and filed with the secretary of the city or town committee. Thereupon, the secretary shall immediately give notice of such withdrawal and of the provisions of this section to the person who filed such nomination paper, and such person may, within twenty-four week day hours succeeding five o'clock in the afternoon of the last day fixed for making withdrawals, present a new name on a nomination paper signed by himself in person; otherwise the chairman and secretary of the committee may file nomination papers for the vacancy. If at any time after the expiration of the time for filling vacancies it shall appear that a vacancy has been created by death, the chairman of the committee may file with the city or town clerk a new name to fill such vacancy; and if the time is sufficient therefor, the new name shall be printed upon the official ballot.
Mass. Gen. Laws ch. 53, § 101