Mass. Gen. Laws ch. 53 § 70G
In case of the death, withdrawal or ineligibility of a candidate for state committee, the vacancy may be filled as provided in section forty-nine.
In case of the death, withdrawal or ineligibility of a candidate for a ward or town committee, the vacancy may not be filled but members may be added as provided in section four of chapter fifty-two.
If there is a tie vote, as defined in section fifty-three, for members of the state committee it shall be filled by the ward and town committees of the district in which it exists.
If there is a vacancy in a ward or town committee caused by a tie or a failure to elect the number provided for in section nine of chapter fifty-two the members elected shall fill the vacancy.
All vacancies caused by ties shall be filled only by the choice of one of the candidates receiving the tie vote.
Mass. Gen. Laws ch. 53, § 70G