Probably because there is no permit required to own those guns in Connecticut just to conseal/carry but records of purchase must be kept by gun shops and they wanted copies of those records for their investigation before they could get lost.
According to the chart below for all the states, there is a requirement for a permit or a license for handguns in Connecticut.
http://www.guardian.co.uk/world/interactive/2013/jan/15/gun-laws-united-states
I looked it up at this site also:
http://crime.about.com/od/gunlawsbystate/p/gunlaws_ct.htm
“•Permit to purchase handgun? Yes
No state permit is required for the purchase of rifles or shotguns. A permit to carry, permit to sell handguns, or handgun eligibility certificate is required to purchase a pistol or revolver.
No state permit is required for the purchase of rifles or shotguns. A permit to carry, permit to sell handguns, or handgun eligibility certificate is required to purchase a pistol or revolver.
A handgun eligibility certificate, valid for five years, shall be issued by the Commissioner of Public Safety within 60 days after receipt of the National Criminal History Records check from the FBI to a person who may lawfully possess a handgun, who completes a handgun safety course, is fingerprinted, and pays a fee.
So I guess technically, it is called a handgun eligibility certificate.
The eligibility certificate entitles a person to purchase, but not to carry, a handgun.”
From the Connecticut State website:
http://www.ct.gov/despp/cwp/view.asp?a=4213&q=494614#eligibility
Eligibility Certificate
An eligibility certificate is issued pursuant to C.G.S. 29-36f through 29-36i. It entitles the holder to purchase a firearm and transport same to their residence or place of business. It does not entitle the holder to carry a pistol or revolver on their person.
Applicants must be at least 21 years old and be a legal resident of the United States. Persons convicted of a felony or any one of 11 misdemeanor offenses detailed in the statute are ineligible to receive an eligibility certificate. Persons convicted as a delinquent for the commission of a serious juvenile offense (as defined in Section 46b-120); persons discharged from custody within the preceding twenty years after having been found not guilty of a crime by reason of mental disease or defect (pursuant to section 53a-13); persons confined in a hospital for persons with psychiatric disabilities (as defined in section 17a-495), within the preceding 12 months by order of a probate court; persons subject to a restraining or protective order issued by a court in a case involving the use, attempted use or threatened use of physical force against another person; persons subject to a firearms seizure order issued pursuant to C.G.S. 29-38c after notice and hearing; and any person who is an alien illegally or unlawfully in the United States, are prohibited from obtaining an eligibility certificate.
The cost for obtaining an eligibility certificate is $35.00, payable to the Treasurer, State of Connecticut. The eligibility certificate is good for a period of five years. The application paperwork may be obtained from SLFU or any state police barracks. You are required to complete a handgun safety course prior to submitting the application, which must consist of no less than the NRA’s “Basic Pistol Course.” The NRA’s “Home Firearms Safety Course” and “First Steps Pistol Orientation Program” are not approved courses.
You will also be required to submit to a background investigation, criminal history check and submit photographs and fingerprints in connection with your application.
The issuing authority has 90 days to review your application and issue an approval or denial. In the event that they deny your application, they must provide you a written explanation listing the basis for denial. A denial may be appealed to the Board of Firearm Permit Examiners as provided under C.G.S. 29-32b.