The only restriction on handguns in CT is the AWB.
Based on a quick internet search the PDP FS4 appears to be a standard modern handgun with the magazine in the pistol grip and the barrel completely contained inside the slide.
On a firearm like this the only way for it to be illegal would be for it to have a threaded barrel, which would make it an assault weapon.
So unless its got a threaded barrel, I don't see a problem.
If you posted pics, even if it wasn't your actual gun, I could give a definitive answer.
Search on the word "threaded". Language inside [brackets] is removed from current statutes by this law.
Relevant text
(iv) A semiautomatic pistol that has an ability to accept a detachable magazine and has at least
one of the following: (this statement used to say TWO of the following: )
(I) An
ability to accept a detachable ammunition magazine that attaches
at some location outside of the pistol grip;
(II) A threaded barrel capable of accepting a flash suppressor, forward
pistol grip or silencer;