N.Y. County Law § 722-C
Upon a finding in an ex parte proceeding that investigative, expert or other services are necessary and that the defendant or other person described in section two hundred forty-nine or section two hundred sixty-two of the family court act, article six-C of the correction law or section four hundred seven of the surrogate's court procedure act, is financially unable to obtain them, the court shall authorize counsel, whether or not assigned in accordance with a plan, to obtain the services on behalf of the defendant or such other person. The court upon a finding that timely procurement of necessary services could not await prior authorization may authorize the services nunc pro tunc. The court shall determine reasonable compensation for the services and direct payment to the person who rendered them or to the person entitled to reimbursement. Only in extraordinary circumstances may the court provide for compensation in excess of three thousand dollars per investigative, expert or other service provider.
Each claim for compensation shall be supported by a sworn statement specifying the time expended, services rendered, expenses incurred and reimbursement or compensation applied for or received in the same case from any other source.
N.Y. County Law § 722-C