As you know, Connecticut does not tax gambling winnings received in the state of Connecticut by a non-resident. However, if Connecticut withheld any state taxes on your gambling winnings (as seen on your W-2G), then if you want that withheld returned to you, you will need to file a Connecticut tax return to get that withholding refunded to you. This is true even if you have no other Connecticut source income.
Of course, if you did not have any withholding on the gambling winnings or the amount is so trivial that it's not worth it to file a Connecticut return to get it back, then don't file a Connecticut return.
The Connecticut interview in TurboTax will recognize that you are a non-resident and will ask you what part of the winnings you believe are reportable in Connecticut. On the same screen, you will see that winnings for non-residents are not taxable in Connecticut, so you are encouraged in the ordinary case to leave the Connecticut field blank (the program will treat this as zero, which is what you want).
