And MPs are demanding answers over the 10 day "gap" before action was taken.
Timeline of suspicious death at James Paget University Puma Ducati
The Home Office post mortem examination was carried out at the Norfolk and Norwich University Hospital (N on Wednesday, October 2.
Senior investigating officer detective chief inspector Paul Durham said: "We are investigating an allegation that a drugs overdose was administered to a patient, leading to his death.
HospitalDetectives who were contacted by the hospital on September 30 are now investigating whether a hospital worker gave Mr May a drugs overdose in the lead up to his death.
"We understand that this news may generate concern and it's important for us to underline that our investigation, which is still at an early stage, is based on a single report of an isolated incident and that the hospital trust is co operating fully with the investigation."
He was bailed that evening until an unspecified date in November, while the investigation continues.
The hospital reported an allegation of medical malpractice in connection with his death to police 10 days later.
Mr May's death is being treated as suspicious and an investigation, led by the joint Norfolk and Suffolk Major Investigation Team, is currently underway.
Therese Coffey, Suffolk Coastal MP, said: "I think it's important for there to be an explanation from the hospital on that time gap."
A middle aged man, described as "a member of the hospital's medical staff", was arrested on Saturday morning on Puma Canvas Shoes Images
Brandon Lewis, MP for Great Yarmouth, said: "I think the hospital has some work to do to clarify why this took 10 days to be reported.
Mr May, who was known as Jimmy, was a divorcee who lived alone in Great Yarmouth.
"A Home Office post mortem, carried out earlier this week, determined the cause of Mr May's death as heart failure and we now await the results of further toxicology tests which will help inform our inquiry.
MPs lead call for answers in James Paget Hospital murder investigation
"I hope it's isolated," added Mr Lewis. "I know the hospital will co operate in any way it can with the police."
A hospital worker came in to the police by appointment on Saturday morning, and was then arrested.
He added it should be made clear whether a whistleblower took days to come forward, or whether alarm bells were sounded immediately but the hospital did not pass the information to police until September 30.
"If there was a whistleblower involved, it's admirable that there was an atmosphere in which that could happen but they need to clarify why it took so long."
But she noted the complexity of the situation, Puma Running Shoes For Men with legal proceedings active.
He added there may be a "perfectly logical explanation" for the period between the death and the police being alerted, but that it is "important that that's addressed".
"One of the difficulties is getting the balance between what they can divulge now and what is reserved for the [police] investigation," she said.
Peter Aldous, Waveney MP, said his thoughts were with the family of Puma Beige Trainers
suspicion of murder.
He had been admitted to hospital the evening before his death, dying soon after in the early hours.
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