In a contemporary interview with People Magazine, De Palma discussed how and why he chose the drill as the murder weapon:
“I do a lot of murder mysteries, and after a while you get tired of the usual instruments. You could use knives, ropes, but now we have electric instruments, which are really scary.”
De Palma also notes there is a reason in the story for the overkill. It turned out that the killer, who was wearing a disguise, want to Jake to take a look. This means Jake will turn over his masked appearance to the police, who will in turn go after someone who isn’t there. A noisy electric drill will definitely attract the attention of neighbors.
In “Back Window”, we don’t see the murder weapon being used, but a knife is suggested. It’s the same weapon used by Norman Bates in Hitchcock’s most famous murder, the shower scene in “Psycho.” De Palma’s “Dressed to Kill” featured other knife-wielding assassins, as well as less mysterious butchers of the era such as “Halloween”.
A drill also has the same phallic symbolism as an ordinary knife, so “Body Double” doesn’t lose the sexual element of its gore. De Palma said that, “no [his] intention” to suggest this by drill, although he acknowledged why anyone would think that. Whether out of his own austerity or the disapproving Hays Code, Hitchcock tended only to suggest violence. De Palma enjoyed it.