NJ follows the general rule.
The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state. You will have to file a non resident NY state return and pay NY tax on the income earned there.. You will also file a NJ full year resident return and calculate tax on ALL your income. NJ will give you a credit, or partial credit, for the tax you pay NY. So, there will be little or no double taxation, but you have the cost and hassle of filing two state returns. Do the nonresident state return first.
If you work in a state without an income tax (e.g. Texas or Florida), there will be no credit, since there was no FL or TX tax. In other words, having worked in a state without an income tax does not get you out of paying state tax on that income, to your home state.
