N.Y. Lien Law § 60
If, in an action to enforce a lien on account of a public improvement, the court finds that the lien is established, it shall render judgment directing the state or the public corporation to pay over to the lienors entitled thereto for work done or material furnished for such public improvement, to the extent of the sums found due the lienors from the contractors, so much of the funds or money which may be due from the state or public corporation to the contractor, as will satisfy such liens, with interest and costs, not exceeding the amount due to the contractor. If it appears in any proceeding in which the state is a party that a claim has been or can be filed against the state in the court of claims, or if it is alleged upon the part of the state that the contractor has breached the contract, then the court may render judgment only to the extent of determining the establishment of the lien or liens, and the amount or amounts thereof.
N.Y. Lien Law § 60