Section 671. General duties of coroner, or coroner and coroner's physician, or medical examiner; additional duties may be directed

1. The  coroner,
  or  if  he is not a physician duly licensed to practice medicine in this
  state, the coroner and a coroner's physician, together, or  in  counties
  in which the office of coroner has been abolished, the medical examiner,
    (a)  shall  make  inquiry  into  unnatural deaths within his county as
  prescribed by law;
    (b) shall make inquiry into all deaths whether natural or unnatural in
  his county occurring to an inmate of a correctional facility as  defined
  by  subdivision three of section forty of the correction law, whether or
  not the death occurred inside such facility.
    2. The coroner shall perform such additional and related duties as may
  be prescribed by law and directed by the board of supervisors.
    3. In  those  counties  in  which  the  office  of  coroner  has  been
  abolished,  the  medical  examiner  shall  perform  such  additional and
  related duties involving exercise of professional skills and training as
  may be prescribed by the board of supervisors and the district attorney.