YES

You can buy online from a licensed dealer, who will ship the gun to a dealer in your area, where the paperwork and background check will be processed. If you buy online from a private seller in another state, they will have to send the gun to your local dealer for you to follow the same process.

If you buy online from a private seller within Connecticut, you can purchase the gun without a background check, and the seller will not have to retain records. Online marketplaces like Armslist connect buyers and sellers.