No. Provided the barrel is not shorter than 12 inches, a pistol permit is not required to purchase a pistol grip shotgun. Note: The ATF has indicated that a pistol grip shotgun cannot be sold to anyone under the age of 21.
A firearm with a pistol grip in lieu of the shoulder stock is not designed to be fired from the shoulder and, therefore, is not a shotgun. Since it is a firearm “other than a rifle or shotgun,” the purchaser must be 21 years of age or older. Additionally, interstate controls apply. The licensee and transferee must be residents of the same State.
GCA, 18 U.S.C. § 921 (a) (5)
Connecticut General Statute Sec. 29-37a.