State tax filing

There are two things that will happen on your NY return.

1. Your tax liability will be calculated based on your income for the whole year. Then, an income percentage will be applied to that tax liability to prorate your tax based on how much income you earned while a NY resident. 

To calculate the income percentage, you will need to allocate the income you earned during the year between your non-NY period and your NY period. Allocate all income earned while you lived in NY to NY, even though you worked in NJ. This income is taxable to both NY and NJ.

2. Your prorated, NY tax liability will include tax on the same income that's taxable in NJ. You'll get a credit in NY for the tax that you paid in NJ.

To make sure this credit is calculated properly, you'll need to click Start or Edit next to Tax Paid to Another State on the Take a look at New York credits and taxes screen. You'll see a screen asking if you'd like to calculate the credit. Click Continue. On the next few screens you'll enter information about your NJ income (if it's not already populated) so that TurboTax can calculate your credit.