No. You need to file both a NY and NJ return. As a resident of NY, you are required to report to the state all of your income, no matter where on the planet that income comes from. Basically, you'll be filing a NJ non-resident return and a NY resident return. It is *IMPORTANT* that you complete the non-resident state return first, and do the resident return last. That way, the program can correctly take into account any reciprocal tax agreements that may exist between all the states involved. In your case, there is such a tax agreement between NJ and NY. So it's vital you complete the NJ non-resident return first, and leave the NY resident return for last.
Also, do not file "ANY" return (including the federal) until after you have completed all returns and are satisfied with the result. For someone in your situation, if you make just one tiny mistake on any one return that later requires you to amend, then chances are high you will be amend all returns, since changes on any one of the returns will most likely affect all the other returns.
