You're on notice, Connecticut.
When I got CT pistol permit way back in 1987 it was an annoying and intrusive process but it seemed mostly a matter of checking the boxes and jumping through the right hoops. No anticipation that a denial was very probable.
Unconstitutional but it was the process.
Sign off by a certified NRA instructor, background check, interview with county sheriff or police chief, don't remember which and I got my permit.
Has it changed much since then?