No.  A mother and father of a child may sign a notarized document called a recognition of parentage, which is then filed with the state registrar of vital statistics, to acknowledge under oath that they are the biological parents of a child.
If the child has a presumed father under a statute, that man may join in the signing of a recognition of parentage form to acknowledge that another man is the biological father.  A joinder like this must be executed within one year of the child’s birth to be valid.
Unless a judicial proceeding determines otherwise, a validly-executed recognition of parentage has the force and effect of a court order establishing paternity.  If there are no competing presumptions of paternity, once a recognition has been properly executed and filed, the court may not allow additional action to determine paternity.  An action to determine custody and parenting time can be started without the need for any formal adjudication of paternity.
A recognition of parentage form is the basis for bringing an action to award temporary or permanent custody, parenting time, child support, and possible contributions toward the mother’s pregnancy and birth expenses.