First, look at the Connecticut (CT) return to be sure you have the correct amount of tax (not withholding) on that return.
As a rule, the nonresident state return should be completed first so that TurboTax knows what to carry to the resident state for the credit of taxes paid to another state on the same income. You can delete the New York (NY) return, complete the CT return and then add the resident state of NY back to your return. The instructions below will walk you through what to do.
In the New York (NY) state return you must select to review the 'Taxes Paid to Another State'.
Go to your NY state return > continue through that return until you come to the following page. 'Take a look at New York credits and taxes'
Scroll to 'Credit for Taxes Paid' > Select Start beside Taxes Paid to Another State'
Continue through the screens and TurboTax will populate the tax paid to Connecticut (CT) on the same income.
Continue through the screens and only change a field if it has the wrong information.
You should select you want the CT return to go with the NY return.
Your credit will be recorded and applied on your resident NY state return. See the screen below for assistance.