It follows fresh investigations into the death of Matthew Leahy, who was found hanged at Linden Centre in 2012.
His mother, Melanie Leahy, said her talks with Essex Police suggested the cases had taken place in the last 17 years.
The Essex NHS Trust said patient safety was a “top priority”.
Essex Police told the BBC’s Victoria Derbyshire programme it was “conducting initial enquiries into a number of deaths which have occurred at the Linden Centre since 2000”.
A full investigation may take place later depending on the outcome.
Matthew Leahy was admitted to the Linden Centre in Chelmsford in 2012 aged 20, after his mental health problems had spiralled following cannabis use. He also suffered hallucinations.
His mother Melanie said staff told her not to go to see her son for the first seven days, to “let him settle on the ward”.
A week later, she was called by a doctor who informed her that her son had hanged himself.
She said he had told her in a text earlier that week he was “in hell”.
Two years later, an inquest concluded Mr Leahy had been subjected to a series of failings and missed opportunities over a long period of time.
“Each patient supposedly has a care plan and it came to light that Matthew had no care plan,” Ms Leahy explained.
“He had no key worker, no-one knew anything for two days. There wasn’t even any observation sheets.”
Following the inquest, the coroner suggested the trust hold a public inquiry into his death – but the trust said it would take funding away from front-line services.
Ms Leahy said Essex Police had confirmed they were “still investigating my son’s death but are also looking at… up to 20 patients, all who died by the same means”.