Lennie is responsible for killing Curley's wife because he did it.
In Chapter 5, Lennie is sitting alone until Curley's wife enters. Both of them start to talk, and Curley's wife launches into a discussion of her own failed dreams. As they talk, the discussion moves into how they both like "soft things" to touch. Curley's wife points to her hair as an example and how she has to brush it over and over. To prove her point about the softness in her hair, she lets Lennie touch it. Excited to touch something soft, Lennie holds her hair and then starts to brush it with his fingers, tightening his grip in the process. Curley's wife struggles and as she does, Lennie's hold becomes vise- like. The escalation causes her to scream, with Lennie panicking and placing his hand over her mouth to silence her. As she struggles to escape, Lennie forcefully shakes her. This causes her neck to break.
As he stares at her dead body, Lennie realizes what we already know. He recognizes that he is responsible for Curley's wife's death: “I done a real bad thing...I shouldn’t of did that. George’ll be mad." Lennie runs away from the scene of the crime because he knows that he "done a real bad thing" in killing Curley's wife.