As far as I am aware, the only persons that can sign off on the cause of death are the Physician, Attending Physician, Medical Examiner, or Coroner - that's what the death certificate says anyway. Washoe County has a Medical Examiner not a Coroner, but other counties have Coroners. Law enforcement does not as far as I'm aware have a say in the cause of death determination, even if they shoot the guy. What I am fairly certain is happening, though, is that they are instructed to treat or report all cases, dead or otherwise, as though they have Covid. That still does not directly impact the stats. The only way it indirectly impacts stats is if the Physician, Attending, or Medical Examiner actively decides it does.
Keep in mind, too, that the death certificate has up to 4 entries to lay out the immediate cause of death, and another part to add significant conditions contributing to death. (I'm looking at a friend's death certificate right now. His used all 4 entries, and no it wasn't Covid.) So you may well have Leukemia (for example) and Covid on the same death certificate. The way the stats work, one does not exclude the other.
What does seem to be showing up in the national stats is deaths in general are up significantly over what would be expected (aka excess deaths). Up a lot more than the Covid death count. I don't know how reliable the expected value is, but probably good enough to call the excess real. More people may be dying because they are avoiding hospitals. Just my speculation, that.