N.Y. Insurance Law § 1101
(b)
(1) Except as otherwise provided in this subsection, any of the following acts in this state, effected by mail from outside this state or otherwise, by any person, firm, association, corporation or joint-stock company shall constitute doing an insurance business in this state and shall constitute doing business in the state within the meaning of section three hundred two of the civil practice law and rules:
(2) Notwithstanding the foregoing, the following acts or transactions, if effected by mail from outside this state by an unauthorized foreign or alien insurer duly licensed to transact the business of insurance in and by the laws of its domicile, shall not constitute doing an insurance business in this state, but section one thousand two hundred thirteen of this chapter shall nevertheless be applicable to such insurers:
(i) where such groups conform to the definitions of eligibility contained in;
(8) Notwithstanding the foregoing, the maintenance of a website outside the state by an unauthorized foreign or alien insurer duly licensed to transact the business of insurance in and by the laws of its domicile, by which a member of a group may self-enroll, through an automated process, in a group life, group annuity, or group accident and health insurance policy or contract, as defined in paragraphs one, two, and three of subsection (a) of section one thousand one hundred thirteen of this article, shall not constitute doing an insurance business in this state, but section one thousand two hundred thirteen of this chapter nevertheless shall apply to the insurer; provided that: