I, Roommate - S1-E3
Other mistake: When the crew are leaving Fry's new apartment, Amy slips on the banana skin again and falls over, and for some reason Fry tries to shut the door without her leaving. Maybe it was easier than drawing her getting up, but still worth a look. (00:15:30)
Answer: You are thinking about episode 20 of series 2 - "Anthology of Interest I". She technically never kills anyone, but in the episode she ask a "What if machine" (one of the Professor's inventions) what would happen if she was more impulsive. The machine then shows the more impulsive Leela killing off the Professor to get the money from his will and thereafter killing Hermes, Bender, Scruffy, Cubert, Nibler, Amy and Zoidberg to cover it up. Finally she does something really impulsive with Fry.
Andreas[DK]