Greetings all!
With all the "stuff" the active guys have to put up with these days, it's good to be retired, isn't it?
I've also experienced LEOSA in two states, CO and AZ. My former employer, Denver, has a retiree shoot one day each quarter to accommodate the old guys. Once a year is sufficient, but they don't mind if retirees want to show up at the other dates during the year for practice. Either revolver or semi is OK and successful qualification covers any firearm. The city concealed weapons coordinator handles the paperwork end and a concealed weapons permit card is issued. It's a different color than the standard permit (which is good for 5 years) and has LEOSA information on it. At the time I retired three years ago, there wasn't much info given to officers nearing retirement about LEOSA. I actually heard about the separate quals from another guy that was leaving around the same time I was.

Arizona is different. The individual can shoot with any department that allows outside retirees or choose from a list of approved instructors. They have separate quals for revolver and semi, so you have to shoot 50 rounds twice to have both on the card. It's also an annual requirement state. The state handles the paperwork and requires a letter from non-AZ agencies verifying status. They don't issue a permit (AZ has those, but doesn't require one for anybody) but instead give you a "firearms qualification card" to keep with your retired ID. All the info is on the Dept of Public Safety web site, including the form that the range officer or instructor signs for you.
Hope this helps someone!