Based on the information you have given and the rules at the link that SweetieJean gave you, you have to file a New York nonresident tax return, in addition to your NJ resident tax return. If you have any New York income at all, no matter how little, you have to file a New York return if your FEDERAL income is more than the New York standard deduction, which it is.
Did you live in New Jersey all year? I'm just wondering because you didn't explain how you had income from Washington while living in New Jersey. If you did not live in NJ all year, your tax filing situation may be a little more complicated.
