N.Y. Workers' Comp. Law § 44
The total compensation due shall be recoverable from the employer who last employed the employee in the employment to the nature of which the disease was due and in which it was contracted. If, however, such disease, except silicosis or other dust disease and compressed air illness or its sequelae, was contracted while such employee was in the employment of a prior employer, the employer who is made liable for the total compensation as provided by this section, may appeal to the board for an apportionment of such compensation among the several employers who since the contraction of such disease shall have employed such employee in the employment to the nature of which the disease was due. Such apportionment shall be proportioned to the time such employee was employed in the service of such employers, and shall be determined only after a hearing, notice of the time and place of which shall have been given to every employer alleged to be liable for any portion of such compensation. If the board finds that any portion of such compensation is payable by an employer prior to the employer who is made liable for the total compensation as provided by this section, it shall make an award accordingly in favor of the last employer, and such award may be enforced in the same manner as an award for compensation.
N.Y. Work. Comp. Law § 44