A shotgun/rifle is not a firearm. They are defined pretty much as a pistol that wasn't registered.Also illegal to own if you are a convicted felon.
To go along with what Spydermonkey said:
UNLAWFUL WEARING OF A BODY VEST
(E Felony)
PENAL LAW 270.20(1)
(Committed on or after Nov. 1, 2001)
(Revised September 19, 2003)1
The count is Unlawful Wearing of a Body Vest.
Under our law, a person is guilty of the Unlawful Wearing of
a Body Vest when acting either alone or with one or more
persons, he or she commits any violent felony offense...2 while
knowingly 3 possessing a firearm, [rifle] [or shotgun] and in the
course of and in furtherance of such crime that person wears a
body vest.
Also residents of Connecticut are prohibited from buying Body Armor unless the sale is face to face (or unless the buyer is a police officer, Police Department, or military).
But in all seriousness if you wear a vest while committing a felony all you will do is get another charge on top of it. And if someone is doing something where they feel they need to be wearing a vest while committing the felony I have a feeling they plan to either die or get away in the end. If they get caught it would probably just be out of injury.