N.Y. Workers' Comp. Law § 46
The employee or his dependents, if so requested, shall furnish the last employer or the board with such information as to the names and addresses of all his other employers during the said twelve months, as he or they may possess; and if such information is not furnished, or is not sufficient to enable such last employer to take proceedings against a prior employer under section forty-four, unless it be established that the disease actually was contracted while the employee was in his employment, such last employer shall not be liable to pay compensation, or, if such information is not furnished or is not sufficient to enable such last employer to take proceedings against other employers under section forty-four, such last employer shall be liable only for such part of the total compensation as under the particular circumstances the board may deem just; but a false statement in the information furnished as aforesaid shall not impair the workman's rights unless the last employer is prejudiced thereby.
N.Y. Work. Comp. Law § 46