James May, 76, from Great Yarmouth, died at the James Paget University Hospital in Gorleston, on September 20. Ten days later, the hospital reported an allegation of medical malpractice in connection with his death.
Detective Chief Inspector Paul Durham, said: "We are investigating an allegation that a drugs overdose was administered to a patient.
"A post-mortem, carried out earlier this week, determined the cause of Mr May's death as heart failure. We now await the results of further toxicology tests."