N.Y. Village Law § 7-734
For the purpose of preserving the integrity of such official map or plan no permit shall hereafter be issued for any building in the bed of any street or highway shown or laid out on such map or plan, provided, however, that if the land within such mapped street or highway is not yielding a fair return on its value to the owner, the board of appeals or other similar board in any village which has established such a board having power to make variances or exceptions in zoning regulations shall have power in a specific case by the vote of a majority of its members to grant a permit for a building in such street or highway which will as little as practicable increase the cost of opening such street or highway, or tend to cause a change of such official map or plan, and such board may impose reasonable requirements as a condition of granting such permit, which requirements shall inure to the benefit of the village. Before taking any action authorized in this section, the board of appeals or similar board shall give a hearing at which parties in interest and other shall have an opportunity to be heard. Any such decision shall be subject to review in the same manner and pursuant to the same provisions as in appeals from the decisions of such board upon zoning regulations.
N.Y. Village Law § 7-734