N.Y. Civ. Rights Law § 6

§ 6. Exemption from military service. All such inhabitants of this\nstate of any religious denomination whatever, as from scruples of\nconscience may be averse to bearing arms, are to be excused therefrom by\npaying to the state an equivalent in money; and the legislature is\nrequired to provide by law for the collection of such equivalent, to be\nestimated according to the expense, in time and money, of an ordinary\nable-bodied militiaman.\n