John Dillinger's Ghost. Where's Does He Haunt?

"Dillinger" the movie, is coming out this week. I remember hearing stories of his ghost haunting the Biograph Theater in Chicago. Very strange story. He was hiding out at his girlfriend place. Because the FBI was on his tail. But, little did he know. She was working for them. Not sure if she was pressured to do so. She was know as "The Lady in Red". Wonder if that song was based on her (I think Desi Arnaz use to sing it). No, not the one from the '80s. But, anyway, she lured him to see a movie. Now, this is when some of this don't make sense? They say he died in the street (there's markers). Then it's said he died on the sidewalk while "trying" to run down the alley next to the theater. So, they believe that the "alley" is haunted by JD. People said that they have witnessed a blue hazy figure going into the alley, fall down, and disappears. It's even said he haunts a bar nearby. What's really odd they don't talk that much about the FBI agent Melvin Purvis. That he was obsessed in capturing Dillinger. He committed suicide after he retired from the agency. But, it's been said he shot himself with the gun given to him when he left the force. Others said it's an accident that happened while he was cleaning it of a tracer bullet lodged inside. Will never know, I guess.