Did Mavis cause the crash that disabled her cousin?

There is nothing to give a definite yes/no answer to this question but based on the conversation I have to conclude that she wasn't involved

Matt Freehauf: When did he get that chair? Sophomore year?
Mavis Gary: Junior. Car wreck. God, he got so much attention.
Matt Freehauf: Yeah, he was the popular cripple. Practically ruined high
school for me.
Mavis Gary: Please. That dick ruined my sweet 16. Same weekend.
Matt Freehauf: You are a piece of work.
Mavis Gary: You're a piece of shit.

Focusing on the way she says, "Please. That dick ruined my sweet 16. Same weekend.", she is focusing on the attention that was taken away from her and given to him. She was the popular girl and she is bitter that one of the most important days in a girl's life was shadowed by someone else.

Breaking down the statement, it implies that it was his fault. "Same weekend" as in "the same weekend I was going to have my sweet 16" implies that she was not involved.

It isn't that she has no remorse, though she obviously doesn't care, but that she is bitter simply because her spotlight was taken away.

I believe that Mike and his back story are simply to give contrast to Mavis and her attitude and to show just how deep it runs.