N.Y. Village Law § 7-700
For the purpose of promoting the health, safety, morals, or the general welfare of the community, the board of trustees of a village is hereby empowered, by local law, to regulate and restrict the height, number of stories and size of buildings and other structures, the percentage of lot that may be occupied, the size of yards, courts and other open spaces, the density of population, and the location and use of buildings, structures and land for trade, industry, residence or other purposes. As a part of the comprehensive plan and design, the village board is empowered by local law, to regulate and restrict certain areas as national historic landmarks, special historic sites, places and buildings for the purpose of conservation, protection, enhancement and perpetuation of these places of natural heritage. Such regulations shall provide that a board of appeals may determine and vary their application in harmony with the general purpose and intent, and in accordance with general or specific rules therein contained.
N.Y. Village Law § 7-700