It is not likely that a court would order sole physical custody to one parent and sole legal custody to another. Physical custody has to do with the day to day decisions regarding the children. Legal custody has to do with the major life decisions, such as education, medical and religious. More often than not, the court will look to grant sole physical custody to one parent and joint legal custody to each parent. If the parents cannot work together on the decisions related to education, medical and religion and this breakdown is having an impact on the health, safety and welfare of the children, than a court is more prone to award sole legal custody to one parent
I think that the Court strides to give the parents joint legal custody, absent an issue of abuse or neglect, to ensure that each has the ability to raise the child, care for the child and be involved in their everyday life.
As counsel above said, it would not make sense to award the legal responsibility to one parent and the physical responsibility to the other. The parent with the day to day care of the child (physical custody) would have to have the ability to make legal decisions. Splitting the responsibility that way would tie your hands in caring for the child.
This is not legal advice and is not intended to create an attorney-client relationship. You should speak to an attorney for further information.