CGS 53a-211(a) prohibits owning, possessing, or controlling "...any sawed-off shotgun that has a barrel of less than eighteen inches or an overall length of less than twenty-six inches" [note that measurements are the same as those used in the NFA] except that [CGS 53a-211(b)] " The provisions of this section shall not apply to person, firms, corporations or museums licensed or otherwise permitted by federal or state law to possess, control or own a sawed-off shotguns or silencers."
(Note that a short barreled shotgun / "sawed-off shotgun" with a barrel less than 12" long (see definition of pistol/revolver CGS 29-27) also requires a pistol permit to possess outside of ones home/fixed place of business outside of the limited exemptions to the pistol permit requirement.]