The first call that goes out when a mysterious death has occurred is (often by law) to the coroner's office. If the death is violent or suspicious, or its cause is simply unknown, the coroner or medical examiner gets to investigate and make an official determination.
The purpose of the investigation is to determine if any criminal or negligent act has occurred. Not all apparent suicides are in fact suicides -- some are accidents (as can occur during autoerotic asphyxiation), and some are concealed acts of foul play. If it's determined someone has died from accidental prescription drug overdose, this enables the police to look into whether or not another person illegally provided the prescription drugs to the deceased.
One of the most elusive murderers to catch is the medical professional who has deliberately overdosed a relatively healthy patient using painkillers. One example is England's Dr. Harold Shipman, who was convicted in 2000 of killing 15 patients by overdose but is believed to have killed as many as 260. When a death occurs in a hospital, many states and counties require the coroner or medical examiner to pin down the cause of death so that intentional acts of malice (or just extreme negligence) don't go unpunished.
As we'll learn next, medical examiners do more than unravel the mysteries of the dead -- they also help the living.