Transferring a firearm via the proper channels in Connecticut is really not a big deal. This applies to family, friends, or others that live in Connecticut. To start, both parties need the appropriate permits.
According to the DESPP web site you are required to fill out 2 forms,
The primary form you need to fill out and sign in quadruplicate is the DPS-3 form. It is a screen-fillable PDF located here dps-3-c.pdf.
The second form is the DPS-67-C - located here dps-67-c.pdf.pdf. This form doesn’t get sent anywhere but is supposed to be kept for 20 years. It’s kind of an affirmation that the purchaser is not a prohibited person etc and you put the authorization number on it (so fill out the DPS-3 first). Although none of us are likely to sell any firearm to anyone we even suspect of being prohibited, if you did that would make you a felon. If the person passes a background check that the SFLU does when you get the authorization number it’s a duplication of effort.
You will need to fill out the seller’s name/address/permit number, the receivers name/address/permit number the make and type of firearm, serial number, caliber and barrel length.
Once that is done call SFLU at (860) 685-8400 and say "I have a person to person transfer" nine times out of ten they will put you on hold, when they come back they will ask for your permit number, the transferee's permit number, they may ask to talk to them. Once they are happy you get an authorization number. Write that down! Enter it on the DPS-3 form and print out 4 copies. Sign them all, have the transferee sign them all.
You keep one for your records,
The purchaser keeps one for their records,
The transferor (you) sends one to SFLU, and
The transferor (you) sends one to the police in the town the transferee he lives in
The best source of information for all this (and more) is on the DESPP SFLU web page located here DESPP-SFLU