In most metropolitan counties and large cities the medical examiner, a forensic pathologist by training and certification, has either replaced the old coroner system, or the medical examiner holds both titles.
I am sure you are right. Still, there is a difference between
cause of death and
manner of death. Statistical summaries do often list suicide as the cause of death, but I suppose they get double counted as "gunshot", "poison", ect.
Barton Keyes must have something to say about this.