It depends. If it is not stated on your W-2 specifically, you will need to prorate the income. In this case, you can divide the number of days you lived in NJ by 366 (the total number of days in 2016), and then multiply this number (to 4 digits) by the amount of NY income. This is an accurate way to determine your NJ income, which you will probably need to enter manually on the NJ part-year return. NJ taxes your income you earned in NY while you were living in NJ also, but will provide a credit for the taxes you pay to NY on this same income.
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