When the county gets involved
Broadly: a death with no physician in attendance, a death that is sudden or unexplained, an accident, or a death in circumstances suggesting anything other than natural causes. In counties with a medical examiner the case goes there; in counties without one, to a justice of the peace.
A death at home from a known illness under hospice care usually does not trigger this, because a physician can certify. A death at home with no recent medical care usually does.
Why it matters more for cremation
Cremation is irreversible, so a medical examiner will not release a case for cremation until they are satisfied no further examination will be needed. That is the same logic behind the 48-hour waiting period in § 716.054, applied to a case that already has a question attached.
A family can sometimes proceed with burial faster than cremation for exactly this reason.
How long
Anything from a day to several weeks. A straightforward release after review can happen quickly. A case requiring autopsy and toxicology takes considerably longer, and toxicology in particular is a laboratory queue no one can jump.
The provider cannot accelerate this, and a provider who implies otherwise is telling you something about themselves.
What a family can usefully do
Give the investigator the medical history quickly and completely — the treating physicians, the diagnoses, the medications. A documented history of the condition that killed someone is often what allows a release without autopsy. Ask for the case number and the investigator’s direct line, and ask what specifically is outstanding rather than how long it will take.
Then let the provider hold the arrangements open. Nothing is lost by having the paperwork ready for the moment the release comes.