N.Y. Comp. Codes R. & Regs. tit. 22 § 25.33
If the position in the noncompetitive or in the labor class held by any honorably discharged veteran of the Armed Forces of the United States who served therein in time of war as defined in section 25.32 of this Part, or by an exempt volunteer fireman as defined in the General Municipal Law, shall become unnecessary or be abolished for reasons of economy or otherwise, the honorably discharged veteran or exempt volunteer fireman holding such position shall not be discharged from the public service but shall be transferred to a similar position wherein a vacancy exists, and shall receive the same compensation therein. It is hereby made the duty of all persons clothed with the power of appointment to make such transfer effective. The right to transfer herein conferred shall continue for a period of one year following the date of abolition of the position, and may be exercised only where a vacancy exists in an appropriate position to which transfer may be made at the time of demand for transfer. Where the positions of more than one such veteran or exempt volunteer fireman are abolished and a lesser number of vacancies in similar positions exist to which transfer may be made, the veterans or exempt volunteer firemen whose positions are abolished shall be entitled to transfer to such vacancies in the order of their original appointment in the service. Nothing in this section shall be construed to apply to a person holding a position designated as confidential or requiring the performance of functions influencing policy. This subdivision shall have no application to persons encompassed by subdivision (a) of section 25.30 of this Part.
N.Y. Comp. Codes R. & Regs. Tit. 22 § 25.33