When I was a student at Troy, the local Sportsman’s Club got the Sheriff to start issuing pistol permits. They told me to go ahead and apply.
The Sheriff’s assistant took my application and every time I stopped by to check, he told me the background check had not come back. After a couple of months the Sheriff’s wife was at the desk and when I asked, she went back and pulled it out and then filled out the form. It cost all of $5 I think.
I later decided that it was the assistant just putting me off hoping I would forget it eventually. I mentioned it to a member of the Club and he said it should not have taken more than a day. He said he would mention it to the Sheriff.
In CT state law requires local PD or to take prints and certain specific documents required specified by state law and subbit to Stare PD to run background checks. If you pass the state/FBI check the local PD is required to issue a temp permit which you bring to the the State PD to exchange for the “permanent” laminated DL style one. IIRC, the temp one is good for something like 30 days and only lets you carry not buy.
Some local PDs will “require” extra documents/steps not specified OR permitted by state law, such as references, home visits, interviews, etc. It;s either play their game or get denied and go before the state to force them to issue it. Of course, theor aren’t any consequences for denying every permit for no reason so they just keep doing it.