The case in question is episode 51 of The Venture Bros.:
Everybody Comes to Hank’s
This is one half of a two-part story from season 4 with each half telling about the summer vacation of one of the titular Venture Brothers. It is like the Venture Brothers version of Tiny Toon Adventures: How I Spent My Vacation. Episode 51 starts with Dr. Venture demanding that Hank get a job over the summer which prompts Hank to starts a chain of small business including working as a private eye. Hank starts with the “case” of his friend Dermott’s mom not coming to pick him up after work. Dermott’s mother almost immediately picks him up but Hank starts working on the much more interesting case of who is Dermott’s unknown father. The gimmick of the episode is that whenever they are on the case everything has a black and white film noir aesthetic and the dialog is the straight out of a hard boiled detective novel.
Reverse Thieves 