I got the request but I do not like the idea of a police station in a cute town where villagers water plants, fish, and visit each others. I even resisted upgrading my house to large, to keep the exterior looking not of place ( my house is by the waterfall to the ocean ). But it seems like a lot of rare items can be found at police station?
I wouldn't mind if I can demolish it later, but I can't.
The guard can tell you if there's a special visitor in town (Gulliver, campsite visitor, Sahara, Gracie etc.) Also, I believe it is one of the only two ways to obtain Sloppy furniture, the other one is villager putting it up for sale at Retail. (of course, I'm not counting the most obvious option: look for the set online)
CurrentlyPlaying: Monster Hunter 3 Ultimate (3DS), Animal Crossing (Dream Code: 4100-2455-0761 for MH monster icon t-shirts), Pokemon X
It doesn't serve much use other than finding out if there's a special visitor in town or sometimes finding rare items in the lost & found. I like it though as its the only way to get Copper or Booker. If you didn't play previous games then you might not care much about them.
If you're worried about it throwing off the "cute" feeling of your town, then get Booker. He's basically a loveable oaf type that gets distracted by pretty seashells when he should be looking for a body washed up on the shore.
I've had my police station for maybe a little over a month now (had the game since June - just took forever to get the request). It's almost useless. I've never gotten sloppy or cardboard stuff from it (or ReTail, but at least ReTail is useful for other reasons). The officer does tell you when some visitors are in town, but you can wander around and find out yourself. I mostly have regular pitfall seeds, stationary, and clothes I already have show up there.
The only rare thing I've gotten there is I've now gotten 2 tricky pitfall seeds over the time I've had it. But I don't care about those anyway.
IMO, the police station is WAY overrated. I'm extremely disappointed by it. I waited so long to get the request for it, and it doesn't do anything for me.