When a proceeding to establish paternity is initiated under this article, the court on its own motion or on motion of any person qualified under article four of this act to file a support petition may direct the filing of a petition under article four to compel the mother to support her child. If the court enters an order of filiation, it may apportion the costs of the support and education of the child between the parents according to their respective means and responsibilities.
N.Y. Family Court Law § 563