You would need several text books to answer this question properly; however here is the oversimplified version:
A mortician is not a medical doctor and a medical examiner is a medical doctor. A mortician is involved with funeral rituals and medical examiners involved in investigating the death. Medical examiners do their work before the corpse goes to the funeral home.
Forensic Examiners do. Typically a forensic pathologist is called in to do an autopsy and perform evaluations as to cause of death, death timelines, toxicology, etc.
If your local Coroner or Medical Examiners Office classifed the death as undetermined, then you would have to hire your own medical expert to conduct your own examination.
Medical examiners determine such things as the positive identification of a corpse, the time of death, whether death occurred at the location where the corpse was found, and the manner and cause of death. They conduct autopsies and other medical tests to ...
William J. Brady has written: 'A chart of the average time of development, eruption and absorption of the teeth' -- subject(s): Teeth 'A physician/attorney's outline of death investigation' -- subject(s): Causes, Coroners and Medical Examiners, Death, Forensic Medicine, Forensic pathology, Medical examiners (Law), Proof and certification
Detectives do NOT determine the cause of death. Depending on the jurisdiction, either a Coroner or a Medical Examiner will make the determination of the cause of death.
This means that some authority, probably a coroner or medical examiner, has determined that a death was not by natural causes. suicide, or accident.
A cause of death may be listed as undetermined. It means that a medical examiner cannot determine whether the death was natural, accidental, a homicide, or a suicide.
Not unless it was an accidental homicide.
Medical Examiners/Forensic Pathologists do autopsies to determine cause of death. Medical students operate on corpses to learn. Morticians open the abdominal cavity to prepare the body for burial.
Homicide - Death at the hands of another person.
Medical examiners are physicians who examine the deceased body for signs of illness, disease, trauma, etc. They look at every organ and at the blood to determine cause of death. An M.E.'s forensic report assigns whether a death was from natural causes or unnatural causes such as accident or homicide. As such, the M.E.'s job is an important first link in the judicial process, helping the non-medical prosecutor to know whether to bring charges of murder or manslaughter. For example, in cases of poisoning over a long period of time, the M.E.'s report not only helps the prosecutor determine homicide (murder) but to decide to make the charge of premeditated murder. In community health aspects, an M.E.'s findings may help pinpoint an area/location that is most affected by a communicable disease, and their work helps establish "death rates" statistics for many causes (diseases, accidents, murders, old age/natural causes) and death rates per the type of disease (example: heart disease due to arteriosclerosis). M.E.s can decide whether there were contributory causes of death as well, which can shed new light on the circumstances and reason the person died.