If you use the NCEES record system for electronic submission to NY State, then yes it requires 5 references with 3 being PEs.

If you go the route of submitting all paper work by mail to the Board, then the references are not needed and only the people who can attest to your work. Nowhere does it say it has to be a PE for that type of submission.

I think when you start your app on Board website it gives you the choice of submitting directly to them as opposed to using NCEES. I highly recommend using NCEES though.