Whenever the owners of 50% or more in frontage on one side of a street or highway in a block or area between intersections of two highways or streets in any district, or a specified part thereof, shall present their signed petition to the Town Board requesting any amendment, supplement, alteration or change in the regulations prescribed for such district, or specified part thereof, it shall be the duty of the Town Board, after public notice and hearing upon such petition, to make a determination upon the matter contained in such petition in accordance with the provisions of § 265 of the Town Law. Any copy of such petition submitted to the Town Board shall be submitted in duplicate, and one original shall be filed with the Town Board.