Hi,
It should look like this one . . . or its blued version. This one is from the same date range, though maybe a year or so earlier than yours.
Folks call 'em "flat latches" due to the different looking cylinder release latches that were phased out around '66 or so.
Ones of this era also came with "diamond" stocks, and the inside of the right stock (grip) would have the serial number (which is also on the butt) written on the stock. The "diamonds" disappeared from later stocks around '68, IIRC.
Hopefully, your dad's M36 still sports its original stocks. It is possible, and they'll possibly be a little smooth on the side of the gun that got rubbed against things while riding in its holster . . . true "beauty marks" that tell a story of its time when it protected your dad from harm on a daily basis.
Mine was obviously owned by a right hander . . . and you can see the wear I'm talking about just below the diamond on the right stock here:
In any event, these little snubbies could be real accurate . . . if the shooter did his job correctly lining up the marginal-sized sights.
Here it is right after I got it, after a trip to the range. I hadn't added the Tyler T-grip yet that makes it easier to shoot. Lots of "old timers" (and others up to this day) swear by the Tyler T-grip . . . but here it is in its "stock" form, and all five shots centered on that little 1" black square target at ten yards . . . excellent accuracy indeed:
You son will treasure this special family heirloom!!!
Here's mine from this era. It is in its original bright nickel plated finish, though many were blued. Some were square butt revolvers though many had round butts like this one. When I'm in a gun shop and spy a vintage Smith revolver with a flat latch or "diamonds" I perk right up!!!