Here in Connecticut the state-level form is the same for dealers as it is for private sales. I don't see a 4473 factoring in anywhere. I don't have a lot of love for most of the firearms laws here, but the Department of Public Safety here is very easy to work with. All you do is call them for an authorization number, they do an instant check on the two parties right there on the phone, and you get your number.
They're also very polite, knowledgeable, and (gasp) return phone calls the same day if you need to leave a message. I also once went down there for a new photo and didn't think my Benchmade folder would be a problem, since it's legal on the street. The State Trooper at the access control point told me I needed to put it back in my car. It seems like in some places they'd have you prone on the ground and in jail in five minutes for the same thing.