I am certainly no expert, but that won't stop me from offering my observations & comments.
First, the m37 is a classic! Well done.
Next, the plain receiver (lack of the hunting scenes on the sides) may indicate military or law enforcement/corrections origin. Plain stock (no checkering) may also support this idea. Yours also appears to be parkerized instead of blued, so that also supports the idea of mil/police/corrections. It looks great.
However, some guns were marked "DSPS" (Deer Slayer Police Special) on the barrel. These barrels are very easily interchangeable and there looks like a very slight difference in the finish between the bbl & tube/receiver so maybe it is not an OG bbl? But if it is a riot gun, considering the 20" barrel, full choke for buckshot would make sense to me.
With a rifled slug barrel using hand cast Lee 1 oz key-drive slugs, mine isn't very accurate. But using 1&1/8 oz Lyman slugs, with my slug barrel & iron sights I can easily hit the 200 yd gong (24" diameter). I reload the Lyman slugs into bulk Wally world shells and this combo really packs a wallop.
From what I have seen, the stock can be prone to crack at the receiver and since yours looks in great shape with little obvious wear on the slide parts, perhaps it hasn't been fired much? That might also suggest a prison origin. However, I would expect rack rash from years of going in & out of gun racks.
Finally, I think you will find that your new meat gun has slam-fire capability.
Nice find! Hope you got it at a nice price.