Mass. Gen. Laws ch. 43 § 102
Except as provided in this section, a vacancy in any elective body shall be filled in the manner provided in section thirteen of chapter fifty-four A. If, under said section, no regularly nominated candidate of the city council or school committee remains, the vacancy shall be filled for the unexpired term by a majority vote of the remaining members, except that if the remaining members fail to fill such vacancy within thirty days after they shall have been notified by the city clerk that such vacancy exists, such vacancy shall be filled by the appointment of any qualified voter of the city by the mayor, or, if there is no mayor, by the vice-chairman, or if there is no mayor or vice-chairman, by the member of the council or of the school committee, as the case may be, senior in length of service, or, if more than one have so served, then the member senior both in age and length of service.
Mass. Gen. Laws ch. 43, § 102