The short answer is: Kind of. The children do not get to decide but are allowed to let the judge know who they would prefer to live with. 

Your child(ren) are allowed to tell the court which parent they want to live with and why. The rule the judge is supposed to follow says that the court must “consider” and give “due weight” to the wishes of children who are of “sufficient age and capacity to reason so as to form an intelligent preference as to custody or visitation.” See Family Code section 3042.

Nonetheless, a child’s participation is a custody determination or custody dispute must be considered on a case by case basis.