I know of no principle of law that is violated when an institution withholds transcripts until an outstanding tuition obligation is paid in full. Seems like a pretty effective device for ensuring that the school gets paid. I have included a link below to an article entitled "Withholding Academic Transcripts and Diplomas" which discusses the subject.
I'm not licensed in New York so don't take what I say here as legal advice. If you need legal advice, please consult a lawyer who holds New York licensure.
The short answer is yes, you have no legal right to specific documents and as a result they may properly hold them till the balance is paid in full, almost ALL institutions do this