What happends to a parent if their child attempted suicide?

Nothing that I know of... the concern is more for the child as attempted suicide is a sign of depression. You may be ordered for family counseling.
I attempted suicide when I was 14... nothing was done to my mother.

Normally nothing, children and family services may do a home study to be sure there is no problems in the home, Also what and why ( from what the child says to authorities) may have some bearing also, if the child says he is doing it becaue he is sexually abused, and so on.

Expect child services to investigate, maybe require counseling for child and so on