N.Y. Village Law § 2-256
If the territory so incorporated as a village includes within its boundaries part of a special district established by the town for a sewer, water, light, fire, park, health, police or any other special district for municipal purposes the territory so included within the boundaries of the village shall not be relieved from bearing its proportionate share of any liability or indebtedness incurred for such special district purposes while such territory was a part of such special district and until such liability is discharged, or such indebtedness paid the proportionate share to which such territory would be liable if it had not been included in the boundaries of the village shall be levied upon, assessed and collected from such territory by the proper officers of such village in the same manner as if such territory had not been included within the boundaries of the village. All moneys so collected shall be paid over from time to time by the village treasurer to the supervisor of the town to discharge such liability. The collector or receiver of taxes of a town and the treasurer of a county shall continue in the execution of his duties in respect to the property included in the boundaries of a village incorporated under the provisions of this article until he shall have collected the taxes authorized or assessed for the year of such incorporation or which have been extended on the town assessment roll and become a lien after such incorporation and pay to the treasurer of the village when collected the taxes extended on the assessment roll against property within the village for highway, health, water, light, fire, park, sewer, police or other special district purposes.
N.Y. Village Law § 2-256