Did you prepare your Federal return in TurboTax? If not, you would need to enter everything from your Federal return in TurboTax, then download the Connecticut state program. When you are ready to file, just file the state return if you already filed the Federal return in a different program or otherwise.
If you are using TurboTax online and completed the Federal return, when you download Connecticut, the Federal information needed will transfer to the Connecticut return.
If you are using TurboTax Desktop, you would need to add Connecticut if you haven't already.