1. (a) personally delivering to and leaving with the Secretary of State, a deputy Secretary of State or with any person authorized by the Secretary of State to receive such service, duplicate copies thereof at the office of the Department of State in the City of Albany, in which event the Secretary of State must forthwith send by registered mail, return receipt requested, one of such copies to the corporation at the address designated by it or at its last known office address within or without the State; or
2. (b) personally delivering to and leaving with the Secretary of State, a deputy Secretary of State or with any person authorized by the Secretary of State to receive such service, a copy thereof at the office of the Department of State in the City of Albany and by delivering a copy thereof to, and leaving such copy with the president, vice-president, secretary, assistant secretary, treasurer, assistant treasurer or cashier of such corporation, or the officer performing corresponding functions under another name, or a director or managing agent of such corporation, personally outside the State. Proof of such personal service outside the State must be filed with the clerk of the court in which the action is pending within 30 days after such service, and such service shall be complete 10 days after proof thereof is filed.

Tax Law, § 216

Every foreign corporation subject to the provisions of article 9-A, except a corporation having a certificate of authority under section 212 of the General Corporation Law or having authority to do business by virtue of section 1305 of the Business Corporation Law, is required to file in the Department of State a certificate of designation in its corporate name, signed and acknowledged by its president or a vice-president or its secretary or treasurer, under its corporate seal, designating the Secretary of State as its agent upon whom process in any action provided for by article 9-A may be served within this State, and setting forth an address to which the Secretary of State shall mail a copy of any such process against the corporation which may be served upon him. In case any such corporation fails to file such certificate of designation, it is deemed to have designated the Secretary of State as its agent upon whom such process against it may be served; and until a certificate of designation is filed the corporation is deemed to have directed the Secretary of State to mail copies of process served upon him to the corporation at its last known office address within or without the State. When a certificate of designation has been filed by such corporation the Secretary of State must mail copies of process thereafter served upon him to the address set forth in such certificate. Any such corporation, from time to time, may change the address to which the Secretary of State is directed to mail copies of process, by filing a certificate to that effect executed, signed and acknowledged in like manner as a certificate of designation as provided in this section. Service of process upon any such corporation or upon any corporation having a certificate of authority under section 212 of the General Corporation Law or having authority to do business by virtue of section 1305 of the Business Corporation Law, in any action commenced at any time pursuant to the provisions of article 9-A, may be made by either: