I live and work in New Jersey. How come I received a W2 for New York as well? Now, how do I file my state tax return for NJ? And do I also have to file a NY state return?

Seems your employer screwed up. If you neither live nor work in NY State then you have no NY state income tax obligation. If in fact your employer has been withholding NY state tax from your paycheck then (a) you should file a NY state non-resident return (form IT-203) to show $0 NY income and get a full refund, and (b) talk to your employer and have them stop witholding NY tax.

If you were not present in NY to work, you do not have any NY income. If your employer has withheld NY taxes, you should file NY return as nonresident showng nil NY income and claim the refund. You should attach a statement explaining that you lived and worked in NJ. Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)