Section 65. A person aggrieved as aforesaid with respect to a tax on property in any municipality may, subject to the same conditions provided for an appeal under section sixty-four, appeal to the appellate tax board by filing a petition with such board within three months after the date of the assessors' decision on an application for abatement as provided in section sixty-three, or within three months after the time when the application for abatement is deemed to be denied as provided in section sixty-four. Such appeal shall be heard and determined by said board in the manner provided by chapter fifty-eight A. The board may enter such order as justice may require in the manner provided in the preceding section with respect to complaints removed from the county commissioners. The remedy provided by this section shall be in the alternative for that provided by section sixty-four in case of a tax on property in any municipality other than Revere or Winthrop.

If any such petition is, after the period or date prescribed by this section, delivered by United States mail, or by such alternative private delivery service as the appellate tax board may by rule permit, to such board, the date of the United States postmark, or other substantiating date mark permitted by rule of such board, affixed on the envelope or other appropriate wrapper in which such petition is mailed or delivered shall be deemed to be the date of delivery, if such petition was mailed in the United States in an envelope or other appropriate wrapper, first class postage prepaid, or delivered to such alternative private delivery service, properly addressed to the board. As used in this section, ''United States postmark'' shall mean only a postmark made by the United States post office.