If you have a SBR with a barrel 12" or less, then it is classified as both a pistol (any firearm with barrel less than 12") AND a rifle (firearm designed to be fired from shoulder), because there is no definition in CT law for SBR.
The reason this becomes a problem is because of the lovely AWB we have in CT, and the "pistol" section.
You can't build a new AR-15 pistol without complying with the below statutes:
Sec. 53-202a. Assault weapons: Definition.
B) A semiautomatic pistol that has an ability to accept a detachable magazine (as in AR-15) and has at least two of the following:
(i) An ammunition magazine that attaches to the pistol outside of the pistol grip; AR-15 has this
(ii) A threaded barrel capable of accepting a barrel extender, flash suppressor, forward handgrip or silencer; AR-15 barrels are usually threaded (but could have a muzzlebreak pinned/welded)
(iii) A shroud that is attached to, or partially or completely encircles, the barrel and that permits the shooter to hold the firearm with the nontrigger hand without being burned; (AR-15s have handguards)
(iv) A manufactured weight of fifty ounces or more when the pistol is unloaded; and That's the big one to deal with
(v) A semiautomatic version of an automatic firearm
Lots of info here:
http://www.jud.ct.gov/LawLib/law/firearms.htm
ETA
If you decide to go SBR under 12" barrel length then it is not a bad idea to put it on a preban lower, then anything goes, provided it has a stock on it.
If you decide you want an AR15 pistol, you will need to go with an Olympic AR pistol (preban), Bushmaster Carbon 15 Type 97S pistol, or the "swiss cheese" Olympic OA98 AR pistol