It is quite possible for a balance due to NY if the withholding is not enough to cover the tax liability. If you are a NJ resident and work in NY, you have NY source of income and you pay income tax to NY. You are a NJ resident and you pay income tax there but you receive a credit on your NJ return for taxes paid to NY.
When you prepare your state tax returns, make sure to prepare the non-resident state first so that the tax credit can carry over to your resident state tax return properly.
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