Hmmm, having moved from CT to AL this year, here are my experiences:
Connecticut, until very recently, was a "may issue" state, but in the real world, just about anyone who was eligible to own a firearm got their permits to carry concealed pistols and revolvers. This was only done for the local permits, which have now been discarded in favor of the temporary state permit. When getting the local permit, some towns wanted you to jump through more hoops than others. For example, in Bristol, CT, I had to get 3 letters of reference, one from someone who had known me for over 10 years, and the Bristol PD did end up calling one of my references.
Some people did get denied local permits, but upon appealing, just about everyone got approved.
Getting the state permit, even back then, was a simple issue once you had your local permit. Just go to the DPS building, ask the friendly guy at the door where the permits and licensing office was, follow his instructions, go to the booth, pay a small fee, get photographed, and get your state permit in 5 minutes.
Ironically, just about anyone who wants to purchase a handgun in CT pretty much ends up getting a concealed carry permit, since the application for getting a permit to purchase a handgun is essentially the same. No sense in wasting time getting the lesser permit when the concealed carry permit removes the need to have a permit to purchase, but it is this very system that has pretty much killed the gun shows in the state of CT.
As for Alabama, it's also technically a "may issue" state, but I have yet to hear of anyone getting rejected who had passed the background check. My guess is that if anyone did get rejected, they probably showed up there in dirty clothes, having not taken a shower for a month, and swearing every other word.
My experience was this: go into the Shelby Country Sheriff's office, smile at the nice lady behind the counter, ask for the pistol permit application, fill it out right there, pay 20 bucks, and sign the card. In and out in 5 minutes.
The permit process varies from one county to another, as in Jefferson County, you have to be a resident there for 6 months before you can apply, but it only costs 10 bucks / year.
After having attended the gun show in Birmingham last weekend, I can honestly say that it's great to be back South, where there are such things as good gun shows...