Legal Custody typically refers to the right and the obligation to make the decisions regarding a child's upbringing, including schooling and medical care. Many states typically have both parents share legal custody of a child.
Duhaime Legal Dictionary
A child custody decision which entails the right to make, or participate in, the significant decisions affecting a child’s health and welfare (compare with physical custody and joint custody).
Lect Law Library
In a divorce, one of two types of child custody. A parent who has legal custody has the right to be involved in all the decision making typically involved with being a parent, such as religious upbringing, education and medical decisions. Legal custody can be either sole or joint. Compare with physical custody.