I work in NJ but live in NY and only NJ taxes were deducted

[ChristinaS]

That's appropriate. Employers withhold for the state you work in (unless there is a reciprocity agreement in place~ which NY and NJ do not have)

In Turbo Tax, prepare your nonresident NJ return before working on the NY return. When done with NJ, switch over to the NY resident return interview.

On your NY return, you will come across a Credit for Taxes Paid to Another State. This credit will reduce or eliminate any taxes owed to NY, as you get credited for taxes paid to NJ.

If your NY tax rate is higher than NJ's (that could go either way, as NY has tax benefits that NJ does not), you may still owe a little bit to NY. However, it would not be common for your NJ employer to withhold NY taxes for you. If you find that you still owe NY, you may want to consider making estimated tax payments to NYS during the year. You would make estimated payments on par with any NYS tax due after the credit for taxes paid.

https://www.tax.ny.gov/pit/estimated_tax/filing_estimated_income_tax.htm