I work in Pennsylvania and do work for New York ( city and state) on a regular basis.
In my experience...
New York City quals are goverened by the NYSSCM (New York State Steel Construction Manual)
I test, (must be witnessed by NY representative) and then get my radiographs graded and signed off by a third party. If all is ok, I forward radiographs to Albany for final acceptance.
New York State (Albany) will review and approve (hopefully) your radiographs.
If you let them know, they will forward results to NYC.
There can be more than that under certain applications.
Do get a copy of the NYSSCM manual. That way you will know for sure what the exact requirements are. The latest edition is from 1984 or thereabouts. Really no new updates. Relatively inexpensive code.
Keep us posted...
brande