It is an M-42 shell, stamped in ventilation holes, flared, unrolled raw edge...
Rough combat finish.
The decals are police, but with the rough combat finish, it surely belonged to a soldier in the 4th SS Polizei Division, or one of the SS Polizei combat regiments....
Its in very good shape, and nice liner....
Its a super helmet, and could be worth a shitload...single decal SS helmets are worth around $4-5k....this is likely worth $2500 and up on the collector market...
The 31C is the steel/heat lot, it is a 66 sized shell (pretty big), and the bkp is the shell manufacturer (don't know it off the top of my head, but can look it up....)
I would get rid of the wire "chinstrap"....the fingers of the liner were held together by a simple piece of string through the holes in the ends. The chinstrap...very nice repros can be found, originals will set you back $150-$250...
If it were mine, I would find a piece of old string and gently snake it through the holes and lightly tie it, and find a really good repro chinstrap, and add it on. That's it. Just dust it, and don't ever touch the shell with any sort of oil, varnish, cleaner, anything...
I'd add it to your insurance....
ETA Oh, and the scratchouts....most likely done to adhere somewhat with the orders that came down in 1942/43 to remove insignia, as they made a good aiming point....that's why the move to single decal helmets, then no decal helmets....field guys were ordered to scratch off the decals, and this was how it was done many times, kind of a token scratch off.