The Office of the Chief Medical Examiner shall complete its investigation where reasonably possible within thirty days. Upon completion of the investigation, the Chief Medical Examiner, Deputy Chief Medical Examiner, an associate medical examiner, an authorized assistant medical examiner or a pathologist designated by the Chief Medical Examiner shall file a death certificate, or a certificate supplementing that already filed, with the registrar of vital statistics for the town in which the death occurred, if known, or, if not known, for the town in which the body was found. If the deceased is unidentified, fingerprints, provided mortification has not proceeded so far or the nature of the cause of death was not such as to make identification impossible, shall be sent by said office to the Division of State Police within the Department of Emergency Services and Public Protection.