N.Y. Comp. Codes R. & Regs. tit. 21, § 5005.1 – Who may file a retirement application.

(a) A member who meets the eligibility requirements for retirement may file an application for service, disability or deferred retirement.
(b) The system shall not be obliged to inquire as to the competency of the member. If the system, however, receives information which, in the system's sole judgment, raises a question as to the member's competency, the system may, in its sole discretion, take such actions as it may deem appropriate including, but not limited to, requiring a statement, completed by a qualified physician, attesting to the member's competence to file a retirement application.
(c) A duly appointed guardian of the person or the property of a member may file an application on behalf of a member, provided such guardian has been authorized to do so by the court which appointed such guardian. A certified copy of the court order must be submitted to the system.
(d) If the application is signed by the member with his or her mark (x), his or her mark must be notarized or must be witnessed by two individuals and, in addition, the following affidavits will be required:
1. (1) an affidavit executed by each witness stating that the mark (x) is the signature of said member, and explaining why the member is incapable of signing himself or herself; and
2. (2) a statement executed by a qualified physician explaining why the member is incapable of signing himself or herself.
(e) An employer may file an application for disability retirement on behalf of a member who is otherwise eligible to retire for disability. A true copy of the resolution of the employer's governing body authorizing the representative of the employer to file an application on behalf of the member must be submitted to the system.
(f) A person may file an application for service, deferred or disability retirement on behalf of a member of the system where such person has been authorized to do so pursuant to a valid power of attorney which has been properly executed pursuant to applicable law. However, the person filing such application may, in the system's sole discretion, be required to prove the member's competency as set forth in subdivision (b) of this section, unless the power of attorney expressly provides that it shall not be affected by the subsequent disability or incompetence of the member and the system determines in its sole judgment that such proof is not necessary or required to protect the system. A copy of the power of attorney must be filed with the system.