live in NJ work in CT - who do I pay taxes to

It depends.

You would need to file a nonresident tax return in Connecticut (CT) if you had any state income taxes withheld or if you meet the gross income test.  Please see the following to determine if you meet any of these thresholds.

If you meet the filing requirement above, you would report your income on a nonresident Connecticut state tax return.  

You would then be able to claim a credit on your New Jersey state tax return for any income taxed in both CT and NJ.

To do this in your tax return, review your entries in the My Info section of TurboTax located in the black panel on the left. 

Confirm that you have entered the correct state information: 

1. Click Edit to the right of your name 
2. Confirm your input under #2 "Tell us the state(s) you lived in" 
3. Do the same for your spouse if you are married filing jointly. 
4. Go back to the personal information section, and verify the mailing address and Other state income section. You would enter Connecticut in this section. 

Review your information in Lines 15-17 in the W-2 input section in the federal income section.  Make sure any withholdings and income are reported by the state they are earned in and as reported on your W-2 form.

Prepare the Nonresident Connecticut state tax return first. Pay attention to the questions to ensure only the income you earned in this state is reported.

Once you have entered all of the Connecticut information, then start your New Jersey return.  This will ensure you receive any credits for taxes on income which may have been taxed in both states.