The New York State Assembly is the lower house of New York State government. Assembly District boundaries change significantly in the years after the release of the decennial census. The current boundaries reflect the 2020 decennial census results.

However the New York City Department of City Planning builds political boundaries from the yearly LION (streets) so presumably boundaries shift slightly based on improvements in the accuracy of the underlying streets data.

Department of City Planning

https://www1.nyc.gov/site/planning/data-maps/open-data.page#district_political

The New York City Department of City Planning serves "State Assembly Districts" as either clipped to shoreline or with water areas included. The "Download" options yield a zipped shapefile named after the current year.

As of 2019 the REST service URL is at http://services5.arcgis.com/GfwWNkhOj9bNBqoJ/arcgis/rest/services/nyad/FeatureServer/0 . Does this change? Only time or a helpful contact from someone at the Department of City Planning will tell.

NYC Open Data

NYC Open Data serves the same datasets. Best to verify that the name of the "Original" file export on NYC Open Data matches the name (ex NYAD_19a) from the Department of City Planning. Or just use the Department of City Planning links above to be ensure you're looking at the most recent data.

https://data.cityofnewyork.us/City-Government/State-Assembly-Districts/pf5b-73bw

https://data.cityofnewyork.us/City-Government/State-Assembly-Districts-water-areas-included-/qh62-9utz

New York State GIS Clearinghouse

For all your New York State Assembly District needs.

https://gis.ny.gov/gisdata/inventories/details.cfm?DSID=1360

https://gisservices.its.ny.gov/arcgis/rest/services/