While there are no townships in NYS, there are 5 coterminous town-villages in NYS, which, for all practical purposes, are townships.
A coterminous town-village is where the town and the village have the same name and have the same exact border and the town supervisor/town board and the village mayor/board of trustees are the same.
Three of the 5 coterminous town-villages are in Westchester County (Harrison, Mount Kisco and Scarsdale), one is in Albany County (Green Island) and one is in Monroe County (East Rochester).
For the NYS definitions of county, city, town, village, hamlet and postal zone, go here:
NYS Geographic Glossary