Military and Police is a part of the model naming that S&W used. As Jack noted they could be purchased by anyone.
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The purchaser may or may not have been some sort of law officer (some departments did not buy and issue firearms, but put that on the officer to do). You probably know as much about its history as anyone being that its been in your family for a while. For a fee (or membership) you can ask for some research in to the original sale but generally what you will learn is the retailer whom it was shipped to.
If you are interested in shooting it, there would be nothing wrong with that. Just be careful with some of the cleaning liquids so as not to damage the plating. My suggestion is to find a range that has some instruction available. You would not go wrong to watch youtube information from "Gun Blue"
multipart series on shooting double action revolver -
starting with part 2., "Paul Harrell" on
negligent discharges and getting some dummy cartridges to practice in a safe location. Did I mention safe location? Pick a location with a substantial backstop (eg brick wall) and where you will never bring live ammo. It is good to be redundent with safety when dry firing - after all it is still pulling the trigger.
A reasonabley good starting video is this one from Chris Baker at Lucky Gunner