Okay, it isn't a strong connection. After John Dillinger was shot outside the Biograph Theatre, my great Uncle Otto--who had been born in Poland but came to the U.S. with his parents-- hopped on his motorcycle to follow the body to the morgue, where crowds of thrill seekers filed past to get a look at the famed gangster. As far as I know, he was not one of those who dipped his handkerchief in Dillinger's blood as a souvenir.
Today's Trib has an article on Dillinger's Haunts, which include several locations in Uptown. The funeral home where he was embalmed is at 4506 N. Sheridan, a gorgeous old building which still stands. It's worth checking out the article, which includes an interactive map.