N.Y. Gen. Mun. Law § 142
In case of the death of a trustee or of his resignation, removal from office, or inability to discharge the duties of his office, his place shall be deemed to be vacant, and may be filled by the remaining trustees; and, in default of their so making an appointment within three months, the appointment to fill the vacancy shall be made by the supreme court, on the petition of any inhabitant of the interested city, village or town, and after due notice to the other trustees and to the mayor of the city, president of the village or supervisor of the town. Said trustees shall be subject to removal by said court for malfeasance or misfeasance in office, upon such notice and after trial in such manner as said court shall direct.
N.Y. Gen. Mun. Law § 142