Babies should stay in the hospital for 24 to 48 hours after the mother gives birth even to a healthy baby so that the nurses can make sure that everything is okay with the baby for those 24 to 48 hours.
However no hospital can force you to keep the baby in the hospital through any legal means.
As long as the baby was born to you then you as the mother have every legal right to remove the baby from that hospital and go home with the baby at anytime you see fit.
You also have a right to have the baby in the same hospital room as you and not be sent to a nursery in the hospital.