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A great deal will depend on the location and circumstances of the death. Every state was different, and in the 19th century few (if any) states kept records of such things and even fewer people would have been inclined to go through the effort of registering such information with the state. Also, autopsies would have been rare and medical knowledge out of date by modern standards, so if someone died of an illness for example even the people that knew him or her wouldn't necessarily have had an 100% accurate knowledge of what illness it was.
The only thing I can suggest at this point is to try the guidance given here: https://www.familysearch.org/wiki/en/United_States_Death_Records