N.Y. Jud. Law § 33
The expenses of an investigation or prosecution in any county of a matter or charge connected with, growing out of or relating to a contract or contracts between the state, or any department, board, commission or officer thereof, and any individual, firm or corporation, if such prosecution or investigation shall have been ordered, directed, or recommended by the governor, the legislature, a joint committee of both houses of the legislature or a committee of either house, shall be borne by the state. Such expenses shall be paid in the first instance by the county, as the expenses of other criminal investigations or prosecutions therein, but the county shall be reimbursed therefor out of moneys appropriated for such purpose. Payments by the state under this section shall be made from the treasury on the audit and warrant of the comptroller to the order of the treasurer of the proper county, upon his certified statement of the items of expenses paid by the county on account of such investigations or prosecutions, accompanied by the written approval of the attorney-general thereon. Such payments may be made at any time during the pendency of any such investigation or prosecution, for expenses accrued and paid by the county to the date of the account, but not oftener than once in three months.
N.Y. Jud. Law § 33