East Haven - Chief Gallo will interview neighbors and his officers will reveal to your neighbors that you are applying for a pistol permit. (invasion of privacy and a safety issue itself if the neighbors are criminals) I know this for a fact, because my mother who lives in East Haven called me to tell me a neighbor on her street was applying for a permit and the officers who came to interview my mother about the applicant's character, spilled the beans to her.
The Chief may also call you into his office for a one-on-one to size you up and he has imposed his own "90-day" wait before they send anything to the FBI. (which technically exceeds the 6-8 week rule that has existed since the days of computer reels and mainframes) And they ask for the three letters of reference (that is old, East Haven always had that rule - I remember going through it when I was 18 back in 1984)
Manchester - Chief James Barry is vehemently antigun. He presented at a gun conference in Hartford that I attended a few years ago.
He stated that he tries to dissuade applicants from getting a permit and bragged about using his NRA instructor rating as a way to counsel applicants AGAINST getting a gun. Chief Barry is a former Hartford police officer. He also stated he was in favor of bans or other restrictions on Ammunition. (He was the only uniformed Chief presenting who wore his duty belt, complete with gun, out of his jurisdiction, while he addressed the press from the podium at the Lyceum center in Hartford where they posted "NO GUNS ALLOWED" signs - intended to deter any pro gunners in attendance. Even Hartford's chief at that time, appeared wearing no visible gun or gun belt.
Berlin - I am aware of people in Berlin getting denials or simple failures to process their requests on a few occasions.
Hamden - another tough city, but not as bad as during the 1970s and 1980s when then chief Ambrosio's name was in the papers virtually every week for being dragged into court over failure to process permit applications. (I believe it was because of Hamden and some other towns that sparked the "reform" in the permit system, getting away from the "Town Permits" and going to the "Temporary State Permit"
New Haven - I am aware of new applicants being flatly refused to even get applications. This has been blamed on the former Chief; but I personally believe it to be a bad case of public relations/customer service on the part of whoever was at the desk that day.
It is not unheard of in cities like Bridgeport and New Haven for the process to take 5 months.
Valley - generally pretty good. Seymour, where my wife used to live before we moved, was good. They have "an application to get an application" process and I believe they run you right then and there, because my wife got a phone call from the Seymour detective handling permits, to pick up her ap - the next day. She had her permit in 3-4 weeks. Naugatuck and Oxford, pretty good - the only problems they have is with smudging finger print cards. I did hear some horror stories about one officer in Naugatuck, but never could substantiate it.
Trumbull - EXCELLENT. Trumbull has the highest number of pistol permit holders (and dues paid NRA members) of ANY city or town in CT. A friend of mine just took the course last month and things are moving smoothly.
I am unaware of specific issues in Eastern Connecticut or the Northwestern corridor of the state.