If the information is pre-filled, you leave it. Otherwise, you have to prorate your NY tax. What you do is first take your total NY tax withheld and subtract the amount of refund (or add the additional amount of tax you owe) to that figure. You then figure out how much of the income was earned in NJ (NJ income divided by total income). Multiply this percentage by the overall NY tax above. This is the amount of tax you paid to NY on income earned in NY while living in NJ. (Income in box will match what you earned in NJ)
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