Mass. Gen. Laws ch. 41 § 10
If there is a failure at an election to choose a town officer, except a selectman, or if a person chosen shall not accept such office, or if a vacancy shall occur, the town may at any meeting elect a person to such office.
If, at an election of town officers for which official ballots are used, there is a failure to elect a town officer, he may be elected at an adjourned or succeeding meeting; and ballots shall be prepared and furnished for such meeting, containing the nominations already made and such as may subsequently be made for the office.
The proceedings in such election and the qualifications of a person to be elected or appointed in case of failure to elect, refusal to accept or vacancy shall be the same as in an original election.
If there is a failure to elect or a vacancy occurs in the office of selectman, the remaining selectmen or selectman may call a special election to fill the vacancy and shall call such election upon the request in writing of two hundred registered voters of the town, or twenty per cent of the total number of registered voters of the town, whichever number is the lesser; provided, that such request is filed with them or him not less than one hundred days prior to the date of the next annual election.
If there is a resignation of a town officer creating a vacancy at some later time certain, and such resignation is filed with the town clerk in accordance with the provisions of section one hundred and nine, said town clerk shall certify a vacancy shall occur at the later time certain and the board of selectmen may call a special election as provided in this section; provided, however, that no such election may be held prior to the effective date of the resignation creating such vacancy.
No election shall be held for any office pursuant to this section unless the selectmen file with the town clerk notice of an election for such office not less than fifteen days before the last day to submit nomination papers to the registrars of voters for certification, before the election or any preceding primary, caucus, or preliminary election.
Mass. Gen. Laws ch. 41, § 10