N.Y. Comp. Codes R. & Regs. tit. 9, § 1727-8.4 – Action by housing company and by the division.

(a) Where a family member applies to the housing company for permission to remain in occupancy the housing company, within 30 days of receipt of the application, shall act upon the application by either requesting the division to approve the application or by denying the application and notifying the applicant family member in writing of its determination.
(b) In the event the housing company should deny such application the notice to the applicant shall set forth the specific reasons for the denial and a statement advising of the method to be followed to appeal the housing company's denial to the division.
(c) A family member applying to succeed to a lease, within 30 days of receipt of the written denial notice, may appeal to the Office of Legal Affairs of the division from such denial by the housing company, by sending the appeal to:
Division of Housing and Community Renewal
641 Lexington Avenue
New York, NY 10022
Attention: Office of Legal Affairs
together with proof of service of a copy of such appeal upon the housing company. The appeal shall briefly set forth the reasons why the family member believes he or she is entitled to occupy the apartment and any errors or erroneous findings he or she believes are contained in the housing company's determination.
(d) Pending a determination by the division on the family member's appeal such family member may continue in occupancy.
(e) In the event such family member is found by the division to be ineligible to remain in occupancy then such family member shall vacate the dwelling unit or the housing company shall proceed to terminate such occupancy pursuant to Subpart 1727-5 of this Part.