HOW LONG DOES ONE HAVE TO FILE A CIVIL SUIT IN OHIO FOR MENTAL ANGUISH

Provided that you have a cause of action and the coroner does not have immunity from civil suits, I believe that your "mental anguish" claim would fall under a claim of "intentional infliction of emotional distress" which is governed by ORC 2305.09.  That section provides that you have 4 years from the date of the incident to file a lawsuit.