can i move my child out of new york state?

Leaving the jurisdiction with your child when you and your former husband have joint custody -- and i assume that he has been seeing the child regularly and paying support -- is the last thing you want to do n NYS without either his consent in advance or Court permission.  Has he said he is opposed?   If not, then you must get something in writing from him, formally acknowledged before a notary public in advance of your move.  If he says no, then you have the option of bringing an application by order to show cause in the Supreme Court which granted your divorce.   That having been said, you need very good reasons to leave -- he has a history of non-payment of support for instance; you can't afford to stay here; you've tried to get a job here and can't (and be able to demonstrate a broad job search), etc.   The case law is very clear that the Courts here do not lightly consider requests to relocation so that reasons why you are seeking to relocate are looked at very closely.