If you live in NYC but work in CT, you will need to file both a CT nonresident state income tax return (to report only your CT sourced income) and an NY/NYC resident state income tax return to report all income (including CT sourced).

You will want to work on your nonresident CT state income tax return first (if you did your NY first, you will want to delete it and start over with the CT nonresident return). You will then take a tax credit from your nonresident CT state income taxes on your resident NY state income tax return. (Please note that you will only get a tax credit for your CT state income taxes up to the amount of NY state income taxes that would have been paid if the income was earned in NY).  The credit for taxes paid to another state section will be at the end of your residence state's interview process.

Just follow the TurboTax guide when working on your states (remembering to do your nonresident state return first) and TurboTax will do all the calculations and credits to your resident states return.

Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)

https://ttlc.intuit.com/replies/3300797