Tracey Arden, from Stockport, and two men, aged 71 and 84, died following the deliberate contamination of saline solution at Stepping Hill Hospital.
Police were alerted when insulin was discovered in a batch of 36 saline ampoules that had been tampered with.
Detectives said the deaths were being treated as unexplained.
Officers are awaiting the results of post-mortem examinations.
Eleven patients who survived the effects of the medication are to be interviewed by police.
Concerns were raised on Tuesday when an experienced nurse at the hospital reported a higher than normal number of patients with low blood sugar levels on her ward.
Continue reading the main storyWe have someone deliberately contaminating saline in the one place that people should feel they are being most cared for”End Quote Assistant Chief Constable Terry Sweeney Insulin was subsequently found in a batch of 36 saline ampoules in a hospital storeroom.
Multiple sclerosis patient Ms Arden, a mother-of-two and grandmother, died on 7 July.
Her parents, Keith and June, visited her on that afternoon but were later called by hospital staff and told she had "taken a turn for the worse".
By the time they arrived back at Stepping Hill their daughter had died.
Ms Arden's funeral has been delayed while police investigate.
Her brother, Gary Arden, said news of the investigation was a shock as the family had initially been told she had died from a lung and chest infection related to her multiple sclerosis.
The contamination of the saline was not restricted to a single ward, the hospital said "We accepted that as a family, that her time had come and that was the cause," he said.
"At this point in time my hope for me and my family is that the investigation takes its due course and we find that Tracey has nothing to do with this. "
The two male victims died this week. The 71-year-old man is believed to have been terminally ill while the nature of the 84-year-old man's illness has not been disclosed.
Greater Manchester Police said it was focusing its investigation from 7 July onwards but would review previous deaths at the hospital if new information came to light.
Increased security measures have been put in place at the hospital to protect patients currently receiving treatment there.
Anyone entering may now be searched and police are interviewing staff and visitors.
Chris Burke, Stockport NHS Foundation Trust's chief executive, said: "We have increased security both in terms of access to the hospital and access to medicines and already replaced all saline ampoules across the hospital.
"We are doing all we can to protect our patients and ensure their safety while under our care."
Assistant Chief Constable Terry Sweeney, of Greater Manchester Police, said: "We have someone deliberately contaminating saline in the one place that people should feel they are being most cared for.
"I want to reassure everyone connected to the hospital - staff, patients, visitors and the wider community - that we are determined to prevent further harm and to bring the offender to justice."
Mr Sweeney said police were still waiting to find out if the contamination of the saline "contributed to the deaths of these three people".
Mark Hunter, MP for Cheadle, said: "This is obviously a very serious matter, I have to say I think the hospital have acted entirely responsibly, acted very promptly calling the police in as soon as they knew there was a problem."
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