The New York City Housing Authority (NYCHA, pronounced "Nite-Cha") is a New York State public benefit corporation with a board that is appointed by the Mayor of New York City. The New York City Housing Authority manages both developments and Section 8 vouchers.

Open Data Portal

https://data.cityofnewyork.us/Housing-Development/NYCHA-Public-Housing-Developments-Map/npwq-dpkb

These boundaries are not perfectly accurate. They may have been digitized by hand around Housing Authority developments using tax lots, possibly from prior years, as a base layer.

The New York City Housing authority has also begun a plan called "Next Generation NYCHA" or "NYCHA 2.0" in which the city allows private developers to build market-rate housing on NYCHA land. This means that, counter-intuitively, new privately owned properties may exist within the polygons of Housing Authority Developments.

This dataset includes 10 developments consisting of Federal Housing Authority Acquired Homes. These records have names like "FHA REPOSSESSED HOUSES (GROUP III)". Each of these FHA records is a multipolygon record with small properties (tax lots, usually) spread across more than one borough. These records are likely to confound your spatial analysis plans unless filtered out or extracted into separate records.