I don't have a police although grew up hunting with a 37 along side my dad with his 37. I have put a ton of shells through both those guns. Great for hunting and that's where it ends for me.
Positives: Light weight, fast shooting, smooth action, great hunting machine, available "slayer" barrel (very accurate)
Negatives: spent hulls hang up on ejector forks, not able to port load, only one pump actuator arm (weak and they can break), only 2 3/4"
Great guns but when it comes to a security gun there are better options. Benelli Nova, Rem 870, Mossy.......
I have one that was an old PD Surplus gun. It had light freckling all over it, so I ended up blasting and refinished it in KG gunkote. In hindsight I wish I would have left it alone and hit it with some steel wool. With that said, the KG turned out great.
Super smooth gun, and luckily none of the internals had any signs of corrosion. It's a slam-fire model too!
They are VERY light guns, and mind has a hard plastic buttplate. I find recoil with full power slugs to be brutal.
I had a 37T Trap Gun many moons ago. One of those "Why did I ever sell that????". Solid Shotgun, light and easy handeling. They made Riot guns for the Military, WWII through Vietnam. These oldies bring a pretty good price with their History.