Yes, this is very possible. But unless it has police markings, acceptance, sear or magazine safeties, then it is hard to prove it was a police.
Many WW1 guns saw weimar, than WW2 service, the 1916 is when it was first made, then the 1920 is the property marking of the Weimar gov't.
Can you tell us any markings on the gun?
Proofs? (see on your left under tech information if you came through
www.lugerforum.com) Tell us what and where proofs and markings are located.
There are forms in this section, where you can print out and then write down pertinent information.
What serial number is on the gun? To include any letters next to or under the serial number?
Can you provide pictures, to include side, top, etc., ?
I collect the Weimar Police Lugers, so they interest me very much.
Ed