A genuine 870P Police gun will be prominently stamped "Remington 870 Police Magnum" on the left side of the receiver.
It will have an aluminum trigger group, usually a parkerized finish, and a short police-length forearm.
If it's new, it'll LOOK new.
The finish will be unworn, there will be no marks on the bolt face indicating it was fired, the inside of the barrel will be clean with no traces of lead or plastic from shot cups.
In will be packed in a green Remington cardboard box with an end label listing the model number and serial number.
If you rub the parkerized finish, you should get traces of a brown rusty looking stain.
This is the coating of cosmoline that Remington sprays the Police guns with as a shipping and storage preservative.
NOTE: You need to remove this cosmoline coating before using the gun. Cosmoline is a storage coating ONLY and in use the metal will rust.
Remington advises to disassemble the gun, including the magazine and spray it dripping wet, inside and out, with Rem-Oil or CLP Breakfree.
Let soak 30 minutes to dissolve the cosmoline, then wipe off the excess lube and reassemble.
This will flush off the cosmoline and impregnate the rough parkerized finish with a rust-proofing lube.
I personally use CLP Breakfree.