Remember, the last scene between the two characters, which is situated before the final act, let fear the worst for her. Now in the living room of Sophia without having been invited, Arthur entrusted him of how disturbing his ill-being – which allowed us in particular to discover that he had fantasized her whole relationship with her, before heading out of his apartment determined to kill.
The answer of Todd Phillips
Good news, if this question haunts you and prevents you from sleeping today, Todd Phillips (the director) officially provide the answer. Interviewed by IndieWire, the filmmaker is explained on the sequence : “He did not kill, that’s for sure. As a filmmaker and screenwriter, I tell you, it does not kill. We love the idea that it is a kind of final test to ensure that the public asks ‘at what point is he crazy ?’.”
A surprise ? On the contrary. It reveals him, it was for Arthur to be a logical choice : “most of The people I’ve talked to don’t think he kills because they include the idea that it kills only the people who had done him wrong. It has nothing to do with it. A lot of people understand that, even as a villain, he lives with a certain code. So, of course, that it does not kill“.
A logical behavior with the Arthur of the film, but less so with the Joker of the comics. This will never be repeated enough, he is a true psychopath, capable of killing everything that moves.