We have them here in the raging metropolis of Greenville, NC -- and they're actually some of the coolest cops you've ever met!
There was a few units responding to our ghetto ex-neighbors having some drama, and I saw the guys with the bike racks, and since they were just sort of extra units on that call, they saw me ride up on my road bike and we hung out and talked bikes for a little bit. Lucky guys get to ride Cannondale bikes. Every now and then you can mayyyybe bait them into a race, but mostly not. You can always tell they want to, though. Like... badly.
They will ride here and there but in warmer weather will mostly patrol our Greenways. They have packs on their bikes with sirens and stuff but they all admit to me none of them want to be "that guy on a bike with sirens wailing." GVegas doesn't have full time dedicated bike units but you can see racks on some of the squad cars and you can tell which guys pull bike duty because they're in killer shape.
It also begs saying that the cops in Greenville who aren't on bikes are some of the best friends cyclists have in this town. I had a crash about a week ago and the responding officer was absolutely awesome. On the road, they'll give you a nod from the car, or that "you okay?" look. They set a really great example for how cyclists are to be treated.