Each case is specific and generalizations are difficult to make. However, the legal rights of parents refusing medical care revolves around the concept of “life threatening” conditions and “life saving” care. Both of these terms can only be determined by a qualified medical professional and must be in accordance to the of standard and scope of practice of his/her peers in the field of medicine.
In most jurisdictions of the United States, a parent is not allowed to sign a child out of a hospital against medical advice (AMA). That is, if a physician is not willing to discharge a pediatric patient because (s)he feels the patient has a life threatening condition, the physician can hold the pediatric patient in the hospital to provide “life saving” medical care. In extreme instances, the physician can remove the child from the custody of the parent.
If they have mental capacity, parents have the legal right to refuse any medical care for themselves even if it is deemed “lifesaving.” However, in most United States courts, parents and legal guardians do not have the legal right to refuse “lifesaving care” for their underage or unemancipated children. For example, a parent may refuse blood transfusions for themselves based on personal preference, religious beliefs, etc. However, if a child is deemed by a physician to have a “life threatening” condition and requires a blood transfusion as the “life saving” care, the physician can provide that blood transfusion despite refusal from the parents.