NY state not recognizing the state tax paid to NJ

[ywjlesley]

So I work in NY and live in NJ. I entered both state tax under federal tax W2 section. In NJ filing I am able to delete the double counting and recognize the NY part of the tax I paid. However, when I file NY under non-resident, I cannot find any place to enter the NJ state tax I already paid so NY is not charging me a very similar and large amount I already paid to NJ. Using Turbotax desktop if it helps.

[MaryK4]

New York does not provide a nonresident credit for taxes paid to another state.  New Jersey provides residents the credit for the taxes paid to another state so you will need to pay tax on the income in New York, then get the credit for New Jersey so that it is not double-taxed.  

See Multiple States—Figuring What's Owed When You Live and Work in More Than One State.