Screwdriver

Doris uses the screwdriver to kill Sue.

Things That Happened
The screwdriver is first seen when Doris attempts to turn herself in to the police, saying she has been hypnotized into murdering someone with a screwdriver. She pulls up her shirt, revealing that her stomach is bandaged, and underneath is a wound with the screwdriver still sticking out. The "Who Is She?" woman killed her husband and then (presumably) herself in a staircase with a screwdriver.

Sue spots the screwdriver in Crimp's yard when he is advancing on her. She grabs it and runs away.

Sue has the screwdriver with her on Hollywood Boulevard while Doris is stalking her. Doris runs up to Sue and grabs the screwdriver, using it to stab Sue to death.

More Things That Happened (Deleted Scenes)
Devon (or Billy) is seen stabbed to death, presumably with a screwdriver.

Trivia
In the Lynch 2 documentary, David Lynch can be seen making the handle for the screwdriver in his workshop.