N.Y. Correct. Law § 16

§ 16. Expense of autopsy; state charge. The reasonable expense of any\ninquiry, autopsy, examination or report prepared thereon conducted by a\ncoroner, coroner's physician or medical examiner as required by law with\nrespect to any death occurring to an inmate of an institution operated\nby the department shall, to the extent not otherwise reimbursed by the\nstate, be a state charge. Reimbursement of such expense shall be made on\nvouchers submitted annually and certified by the chief fiscal officer of\nthe county or city as the case may be on the audit and warrant of the\ncomptroller.\n