By law, can the father take the baby from the hospital if mom got a CPS case?

The father would only have parental rights if he established his paternity. A common way this occurs if both the mother and the father signed a Declaration of Paternity at the hospital when the child is born. Another way to establish paternity is to file a Petition with the court to establish a parental relationship. If you need to request DNA testing, you must obtain a court order before the child is two years old.