Unless the rules have changed, you merely need to show proof of residence to obtain a hunting license. Proof of residence can be a driver's license, but that's not needed. You can use your lease, a pay stub, or a utility bill (cable/phone/electric).

You will need to either have a CT firearms course or a certificate/license from a state that sponsors a course (such as NY or MA).

But no, in essence, once you have a hunting license you can purchase a firearm. With the new laws, I'm not sure what procedures are in place for those without...I believe there is a longer holding period, maybe 10 days (?).

Best place to call is Hoffman's Gun Center in Newington, great guys.