Yes, you may. It is a little complicated, though. You will have to Allocate the amount of income you earned in New York. Click on the following link for the Instruction Booklet for NY Nonresident return. The allocation rules are on page 19: https://www.tax.ny.gov/pdf/current_forms/it/it203i.pdf. There is an allocation screen in TurboTax for the New York return. What you do is figure out the number of working days (do not include weekends, holidays, etc.) that has been used to calculate the New York income on your w-2, and then input the number of days you actually worked in New York. New York has a wrinkle to this. If you were working from home, New York considers you as having worked in New York. If you were in a regular office, though, you were not in New York.
Regardless, NJ will tax all of your income as a NJ resident. They will, however, give you a credit for taxes you pay to NY.
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