If you can find the small town of Carrabelle, FL on the map, you'll find the world's smallest police station.
I know, I know, it looks like a phone booth. And it is. In the 1940s and 50s, the local police had to make calls from a call box mounted on the side of building, outdoors. Meaning, when it was pouring rain, they got soaked. I'm not sure why some better solution to this rather Green Acres situation wasn't contrived earlier, but they finally got the phone company to give them an actual phone booth for their hot line.
The police kept having problems with ordinary citizens wandering into the booth to make phone calls of their own. Rather than put a door with a lock on it, they ended up taking the dial off the phone. Then some nut eventually ripped the phone out completely, and then somewhere down the line somebody finally said, "you know, maybe this has been a really stupid idea."
Since the phone booth was a technically an indoor structure in which policemen conducted official business, this qualified it enough - at least to the local tourism bureau - to call it a police station.