text: Not specific to LA but I was a path assistant in IL and it was if you die in custody, within 72 or 96 hours after a surgical procedure, if investigating officials deem it undetermined, a special ward of the state, children under the age of 12 or 16(i forget) if not determined natural/accidental or if the family asks for one.  There are different type of autopsies as well, full (usually for murder or suspected murder), cranial only (usually to rule out infectious disease), semi full, and trunk only, investigators can ask for specific tests as well for example they found x at the scene and want to test the body for that.