N.Y. Workers' Comp. Law § 53
An employer securing the payment of compensation by contributing premiums to the state fund shall thereby become relieved from all liability for personal injuries or death sustained by his employees, and the persons entitled to compensation under this chapter shall have recourse therefor only to the state fund and not to the employer. An employer shall not otherwise be relieved from the liability for compensation prescribed by this chapter except by the payment thereof by himself or his insurance carrier. The provisions of this section shall not apply to the state of New York, as an employer except to the extent that the fund has provided insurance coverage on an actuarially sound basis to the state pursuant to the provisions of section eighty-eight-c of this chapter. To the extent that the fund has not provided insurance coverage on an actuarially sound basis pursuant to section eighty-eight-c of this chapter, any state employee or other person entitled to compensation under this chapter as a consequence of personal injuries or death of a state employee shall have direct recourse therefor only to the state.
N.Y. Work. Comp. Law § 53