I am not wrong, you do in fact need a permit to purchase in CT (at least you have since 1996) if you don't have a permit it's called an eligibility certificate, let me show you the statute without the mumbo jumbo that clouds this:
Sec. 29-35. Carrying of pistol or revolver without permit prohibited. Exceptions
(a) No person shall carry any pistol or revolver upon his or her person, except when such person is within the dwelling house or place of business of such person, without a permit to carry the same issued as provided in section 29-28. The provisions of this subsection shall not apply to the carrying of any pistol or revolver by
any person transporting a pistol or revolver in or through the state for the purpose of taking part in competitions, taking part in formal pistol or revolver training, repairing such pistol or revolver or attending any meeting or exhibition of an organized collectors' group if such person is a bona fide resident of the United States and is permitted to possess and carry a pistol or revolver in the state or subdivision of the United States in which such person resides,
For the purposes of this subsection, "formal pistol or revolver training" means pistol or revolver training at a locally approved or permitted firing range or training facility, and "transporting a pistol or revolver" means transporting a pistol or revolver that is unloaded and, if such pistol or revolver is being transported in a motor vehicle, is not readily accessible or directly accessible from the passenger compartment of the vehicle or, if such pistol or revolver is being transported in a motor vehicle that does not have a compartment separate from the passenger compartment, such pistol or revolver shall be contained in a locked container other than the glove compartment or console.
Nothing in this section shall be construed to prohibit the carrying of a pistol or revolver during formal pistol or revolver training or repair.
Notice in what I made the second paragraph it states it is ok to transport only if the person, "is a bona fide resident of the United States and is permitted to possess and carry a pistol or revolver in the state or subdivision of the United States in which such person resides," this means no CT permit and a resident of CT you cannot transport in CT.
The final sentence, "Nothing in this section shall be construed to prohibit the carrying of a pistol or revolver during formal pistol or revolver training or repair." Refers to the possession of the gun if you are training or repairing the gun, for example if I took you to the range and let you use my gun, it is legal for you to possess it at that time.