Children often ask to change places between the custodial and non-custodial parent. As has already been stated, a request from a child to do so isn't considered a change in circumstances to warrant a change in court-ordered custody arrangements.
How old is this child? WHY does the child want to live with the other parent?
Keep in mind that many adolescent or teenage kids decide that the custodial parent is mean, doesn't let them do what they want, or makes them do the things they don't want to do. That's just good parenting, NOT a reason to move in with the other parent, who often is the laid-back, more compliant parent when it comes to allowing that child to do what they want during visitation times.
Bottom line? Just because the child WANTS to change the living arrangements doesn't necessarily mean that it's in the child's best interest to move forward with such a change. A court would need to see a significant change in circumstances that favor such a change in custody before ordering it. And while an older child's wishes may be considered, depending on the reasons, they won't be the sole determining factor in granting a custodial change.