Chicago Genealogist 40:2 (Winter 2007) includes an article by Mary Penner on "Using Coroner's Records." The article notes that rules governing deaths and the handling of corpses in various European countries were sometimes exceedingly complex, and fines for rule-breaking so large, that villagers would sometimes drag the bodies of strangers who died expectedly to nearby villages so as to avoid contact with the coroner and his onerous rules.
The coroner system currently in place in the U.S. varies from state to state. Some states require coroners to have medical training, others do not. Coroners who are not doctors can hire a physician as needed to perform autopsies. You can find summaries of each state's system here:
Centers for Disease Control