There is no permit required in CT to buy a gun. Nor is there any registration requirement for said guns.
Oh no, Time missed details or lied?
That doesn’t appear to be accurate:
http://www.ct.gov/despp/cwp/view.asp?a=4213&q=494614
http://crime.about.com/od/gunlawsbystate/p/gunlaws_ct.htm
http://www.guardian.co.uk/world/interactive/2013/jan/15/gun-laws-united-states
According to this chart, you need a permit or a license for a handgun.
Handguns require a pistol permit, long guns don’t IIRC.