While you can find out about a weapon's origins is through law enforcement channels (i.e. the Bureau of Alcohol, Tobacco, Firearms and Explosives, or the ATF), it is possible to find out about a Walther gun by doing some savvy online searches yourself. Bear in mind that because you are choosing an alternate route, there is a margin of error in the results that you receive. Fortunately, given the historical background of Walther pistols, there are books available that list many of the serial numbers of the guns that were produced by Walther.
Find the gun's serial number. The serial number can be located in any one of several places on the gun, depending on which gun you possess. It may be on the frame of the gun, above the trigger guard or on the grip. On Walther pistols, the serial number will generally be located on the left-hand side of the slider. If you have any trouble locating the serial number for any reason, you can bring the gun into your local gun shop for help.
Pick up a copy of either E.J. Hoffschmidt's "Know Your Walther PP & PPK" or Gene Gangarosa's "The Walther Handgun Story: A Collector's and Shooter's Guide." Either one of these books will contain an index of serial numbers for Walther guns. Keep in mind Hoffschmidt's book was written circa 1975, so it will have information that is more dated. Gangarosa's book, which came out in 1999, will have information that is more current.
Perform a serial number search online. There are a couple of websites that offer this type of search. Be aware these sites focus specifically on stolen weapons. StolenWeapon.com has two search fields. One search field focuses specifically on stolen weapons, whereas the other search field is more general. You will need the exact serial number to find the correct result. An alternate site that offers serial number lookups for stolen firearms is HotGunz.