N.Y. Fam. Ct. Act § 514
The father is liable for the reasonable expenses of the mother's confinement and recovery and such reasonable expenses in connection with her pregnancy as determined by the court; provided, however, where the mother's confinement, recovery and expenses in connection with her pregnancy were paid under the medical assistance program on the mother's behalf, the father may be liable to the social services district furnishing such medical assistance and to the state department of health for medical assistance so expended. Such expenses, including such expenses paid by the medical assistance program on the mother's behalf, shall be deemed cash medical support and the court shall determine the obligation of the parties to contribute to the cost thereof pursuant to subparagraph five of paragraph (c) of subdivision one of section four hundred thirteen of this act.
N.Y. Family Court Law § 514