N.Y. Const. art. VI, § 29

a. The legislature shall provide for the allocation of the cost of operating and maintaining the court of appeals, the appellate division of the supreme court in each judicial department, the supreme court, the court of claims, the county court, the surrogate’s court, the family court, the courts for the city of New York established pursuant to section fifteen of this article and the district court, among the state, the counties, the city of New York and other political subdivisions.

b. The legislature shall provide for the submission of the itemized estimates of the annual financial needs of the courts referred to in subdivision a of this section to the chief administrator of the courts to be forwarded to the appropriating bodies with recommendations and comment.

c. Insofar as the expense of the courts is borne by the state or paid by the state in the first instance, the final determination of the itemized estimates of the annual financial needs of the courts shall be made by the legislature and the governor in accordance with articles four and seven of this constitution.

d. Insofar as the expense of the courts is not paid by the state in the first instance and is borne by counties, the city of New York or other political subdivisions, the final determination of the itemized estimates of the annual financial needs of the courts shall be made by the appropriate governing bodies of such counties, the city of New York or other political subdivisions.