To be IAW the FLEOSA different states & municipalities have different systems/training requirements.
There is a basic list of standards & qualifications a LE officer must meet.
Note; President Obama signed into federal law changes to FLEOSA to include some federal LE positions & active duty(retired-qualified) military personnel who served in law enforcement or criminal investigations during their careers(service). This includes; DoD/083 police, rail road/AMTRAK police, US Army CIDC special agents, NCIS, USAF/OSI(Office of Special Investigations), MPs, USAF/Security Forces-SPs, Navy MAAs, US Coast Guard. This new FLEOSA change was in 2013.
I'm not fully versed in LEOSA but from what I know a retired, not just part-time or "off duty" officer/trooper/agent must:
1) be fully sworn with arrest powers & trained/authorized to carry duty firearms
LEOSA does not specify anything about full time, part time, reserve, etc, only that you are/were - "authorized by law to engage in or supervise the prevention, detection, investigation, or prosecution of, or the incarceration of any person for, any violation of law, and has statutory powers of arrest or apprehension under section 807(b) of title 10, United States Code (article 7(b) of the Uniform Code of Military Justice)"
2) must have served a min of 10/ten continuous years with the same dept or LE agency. Breaks in service, suspensions, lay-offs, reductions in force(RIFs) do not count.
You do not have to have all of your time with one dept, you need a minimum total of 10 years, it doesn't have to be consecutive.
3) officers or agents must be fit for duty to use LEOSA & must still meet all agency requirements for carry or use of a authorized sidearm. The retiree/medical related separation can't have a diagnosed mental health or disqualification re; medical problem then get LEOSA certification.
You only have to pass their firearms qualification course. There is no requirement to be "fit for duty". A medical retirement due to service related injury exempts you from the 10 year minimum.
4) the officer/trooper must be able to operate the firearm & pass yearly or mandated training standards as set by the FLEOSA agency. To my knowledge the retired officer/service member must use the same duty weapon they trained on or what they qualified with prior to retirement or formal separation. for example; if the officer was issued a Beretta M9 9mm or M11(SIG P229) then they must qualify & carry a M9 or SIG P228/P229. A LEOSA member couldn't qualify on a Glock 17 9mm then carry a sub compact 26 pistol for CCW.
You must pass the issuing dept's weapon qualification annually. You DO NOT have to use the same gun you carried on duty, you do not even have to carry the same gun you qualify with. You qualify with what you want then you may carry any weapon of that type - semi-auto, revolver, etc.. For instance, if you qual with a 1911 you can carry any semi auto, qual with a M19 you can carry any revolver. Also, LEOSA only specifies what CANNOT be carried - machine guns, silencers, and destructive devices - so you can qual with rifles or shotguns and be covered if you carry a loaded long gun in your vehicle, etc.
5) Some states & locations permit using duty grade or LE type pistol ammunition(JHPs or hollow point) but other places(like New Jersey) might require retirees/LEOSA to meet the same requirements as a private citizen/gun owner. Meaning no JHPs in handguns meant for CCW.
One of the 2011 amendments to LEOSA addressed ammunition - "includes ammunition not expressly prohibited by Federal law or subject to the provisions of the National Firearms Act" - which exempts active and retired/separated officers from state law like NJ's hollow point ban.
LEOSA does not, however, address magazine capacity, so if your carrying under LEOSA you are subject to local mag capacity laws.
6) if a LEOSA member does not meet these requirements or maintain the standards(arrests, drug-alcohol issues, can't qualified with sidearm) then they are no longer in the LEOSA.
The law's text spells out the requirements for annual quals, carrying under the influence of drugs or alcohol, and legal weapons possession, it says nothing about arrests.
I'm not a sworn LE officer. I served in the military police(four years) & stay in contact with a few MPs & CIDC agents thru social media.
I'd suggest obtaining details & requirements from your state's public safety or licensing/occupational standards board. CT regulates LEOSA and has detailed information for retirees/ex-cops who may want to carry in the state.
NOTE some places like CT may restrict what sidearms or models you can use. They won't allow any SAO or single action pistols like Hi-Powers/1911s.
Even if the LE agency allowed it or let the sworn officer/detective pack it during their service.
I read CT's page on LEOSA and qualifying as a resident of CT. Those rules do not apply to a resident of another state that qualified in their home state. For instance, I live in Maine, I am a retired LEO, I qualify under Maine's rules, I can go to CT and carry even if it does not meet their requirements for their residents. Also, because LEOSA does not specify calibers, action, etc., I'm not sure that CT's limitations on those things would stand up to a challenge in court. Just like NJ does not allow their retired officers to carry hollow point ammo, since LEOSA allows it, NJ's law may not stand up in court if challenged.
Also, CT does not allow SA revolvers, SA autos are allowed.