One Huge Lurking Question Which May Make No Sense...MAJOR SPOILER!!!

Okay, we know that the Bat had previously perpetrated several murders locally, and that he was "up to his old tricks." At the very end of the film it is revealed that Officer Anderson was in fact the Bat. His motivation was that he suspected or knew that the missing million was in the house.

Thing is, the money wasn't discovered missing until the beginning of the film, after Cornelia arrived. What, then, was the motivation for all the earlier murders, assuming Anderson was the ONLY Bat? Was Anderson actually a deranged serial killer mainly targeting women, or was he a copycat killer trying to frame the Bat for his crimes?

Do the book, the play, or the earlier two movies shed any light on this? It is sure never mentioned in this movie unless I saw a copy with a scene missing. Left me with one major question! IS THE REAL (ORIGINAL) BAT STILL OUT THERE? If so, nobody is out of danger!