The current Connecticut General Statues appears to indicate a pistol permit is required for any "firearm" that has a barrel less than 12 inches. However, you will get many differing opinions, and there is currently much debate on various firearm discussion boards, with respect to the meaning and interpretations of current Connecticut General Statues on this subject.
Currently, Connecticut General Statutes § 53a-3 (18) define a "pistol" or "revolver" as follows: "Pistol" or "revolver" means any firearm having a barrel less than twelve inches. And currently, Connecticut General Statutes § 53a-3 (19) defines a "firearm" as follows: "Firearm" means any sawed-off shotgun, machine gun, rifle, shotgun, pistol, revolver or other weapon, whether loaded or unloaded from which a shot may be discharged.
And with very few exceptions, carrying of a pistol or revolver is not permitted without a permit. See Connecticut General Statutes Sec. 29-35. for more information and exceptions.