Mass. Gen. Laws ch. 40A § 16
No appeal, application or petition which has been unfavorably and finally acted upon by the special permit granting or permit granting authority shall be acted favorably upon within two years after the date of final unfavorable action unless said special permit granting authority or permit granting authority finds, by a unanimous vote of a board of three members or by a vote of four members of a board of five members or two-thirds vote of a board of more than five members, specific and material changes in the conditions upon which the previous unfavorable action was based, and describes such changes in the record of its proceedings, and unless all but one of the members of the planning board consents thereto and after notice is given to parties in interest of the time and place of the proceedings when the question of such consent will be considered.
Any petition for a variance or application for a special permit which has been transmitted to the permit granting authority or special permit granting authority may be withdrawn, without prejudice by the petitioner prior to the publication of the notice of a public hearing thereon, but thereafter be withdrawn without prejudice only with the approval of the special permit granting authority or permit granting authority.
Mass. Gen. Laws ch. 40A, § 16