N.Y. Pub. Hous. Law § 33
Officers and employees of any board or department in or of the municipality, selected by the authority, who shall theretofore have passed a civil service examination with reference to the position they then hold, may be transferred with the consent of such board or department to the authority, and shall be eligible for such transfer and appointment, without examination, and their salaries or compensation shall, during the effective period of such transfer, be paid by the authority. The officers and employees of such municipality transferred to the authority pursuant to the provisions of this section, who are members or beneficiaries of any existing pension or retirement system, shall continue to have the rights, privileges, obligations and status with respect to such system or systems, but during the period of their employment by the authority all contributions to any pension or retirement fund or system on account of such officers or employees which would, except for such transfer, have been paid by such municipality, shall be paid by the authority; and all such employees shall have the same status with respect to their positions after transfer to the authority as they had under their original appointments. Any employee so transferred may be removed by the authority in accordance with the provisions of the civil service law.
In addition to the right of reinstatement that such persons so transferred shall have pursuant to the provisions of section thirty-one of the civil service law under the circumstances, and in the cases provided in said section, such person shall have the right of reinstatement pursuant to said section not only in the service of the authority but also in the service from which such person was transferred.
N.Y. Pub. Hous. Law § 33