I don't know what the rules are now, for sure, but about 10 years ago, S.O. in Washington had to carry company guns, not personal guns, and both companies that I worked for specified .38 Special ammo. At one company, there was simply no choice as to what gun you carried, they gave you an old 4" S&W at the beginning of each shift, and it was loaded with 158 grain RN (This was actually a nationally known armored transport outfit).
At another company, you could buy your own gun, but then you leased it to the company, so it was their's on paper, but you could keep it when you left the company. In the meantime, it stayed in a locker at work when you were off duty. When each guy went out the door at the beginning of shift, his gun was loaded with standard issue .38, but many of us bought .357 mags, and ammo was promptly changed over in the patrol car.
Even the "unarmed" security at that company carried, but they were very careful about concealing it. They weren't licensed to be armed, but they worked jobs that put them in harm's way, so there just wasn't much choice. Of course, we worked with police all the time, and it wouldn't have been good for an "unarmed" officer if a cop spotted his gun. It's one thing to have to act to save your life, and then face the aftermath, but it's another to get thrown in jail just for being prepared to save your life.
On my college campus, none of the officers were allowed to carry, and I don't believe that many of them ever attempted to. Their job was to observe and report, while not putting themselves in danger. They were issued Kevlar vests, radios, and mag-lights, nothing else. Most training was for first aid or fire response, not self-defense. Even the self-defense training they did receive focussed on when and where you can legally belt someone with a flashlight, without having the university get sued.