Zzyrk's answer is correct, but there is an additional nuance in play here.
Officials are waiting on autopsy results.
To me, this implies that the officials need to receive the autopsy results because the results will allow them to continue their work. The autopsy results are key to the next step in their process, and they cannot continue until they have received them.
Officials are waiting for autopsy results.
This sentence brings to mind an image of some police officers standing outside the morgue waiting for the medical examiner to bring them the autopsy results. It is an activity or a job: their current status or task is "waiting for the results", while the rest of the officials are doing other things.
In this case, "waiting on" implies more that the results are necessary to the rest of the investigation, and the officials can't make any more progress without them. "Waiting for" implies that the officials need the results and will find them important, but they aren't prevented from doing other work until the autopsy results arrive.