The Independent Police Complaints Commission (IPCC) made a series of mistakes in investigating the death of a man in custody, a review has found.
Sean Rigg, 40, who had schizophrenia, died at Brixton police station, south London, in August 2008.
An IPCC report ruled out disciplinary action for police. But an independent review was ordered after an inquest found officers used "unsuitable force".
The IPCC accepts the new report, which recommends charges are reconsidered.
Mr Rigg was arrested in Balham, south London, after he had earlier been found walking topless in the middle of the road, performing martial arts moves.
He was apprehended after members of the public reported that he had briefly attacked a man.
The arresting officers restrained Mr Rigg for several minutes on the ground and then took him to the police station.
The review - led by criminologist Dr Silvia Casale - was commissioned by the IPCC to take another look at its own investigation and report, described by Mr Rigg's family as "extremely poor and ineffective".
Publication of the original IPCC report, which had been completed many months earlier, was held back until August 2012 when the jury in Mr Rigg's inquest delivered its verdict.
Findings included that the manner of restraint had contributed to Mr Rigg's death.
Dr Casale's report recommends, "based on the accumulated evidence following the inquest", that the IPCC "reconsider the conduct of the police officers involved in the apprehension, restraint and detention of Mr Rigg, in relation to possible breaches of their duty of care, with a view to determining whether to bring misconduct proceedings".
It said the IPCC had made basic mistakes, including failing to properly investigate CCTV footage at the police station.
The report calls on the IPCC to look at the length of time Mr Rigg was restrained in a "prone position" and how well he had been looked after when he was in a police van.
And it asks the IPCC to reconsider claims by four officers that they did not know Mr Rigg was mentally ill, despite his strange behaviour and repeated past contact with police.
The report said the officers found his passport, incorrectly assumed it was stolen and failed to run background checks to find out his identity.
When officers were later questioned by the IPCC about why this had happened, Police Federation representatives present had behaved "inappropriately" in batting off questions, the report found.
Metropolitan Police Federation chairman John Tully told BBC News he could not comment on the case because of "other ongoing matters that I would not wish to influence".
But he said the federation would "carefully digest" the report's recommendations to see if there was "any organisational learning that will improve the way we deal with our members in such circumstances".
The IPCC report had concluded there was no evidence to contradict the officers' account that they had not realised Mr Rigg was mentally ill.
But Dr Casale's report concluded: "The review considers that there was ample evidence at the time to suggest that this assertion was improbable."
Dr Casale told BBC Radio 4's Today programme: "It is fair to say that, in 2008, the job wasn't being done as well as it could have been done."
But she said that, while their were "still issues of resources... the indications are that there has been real improvement".
Mr Rigg's sister, Marcia, said the family had concerns about the IPCC investigation from the beginning and had to fight just to get the commission to interview the officers involved.
"It was difficult for us understanding why they couldn't interview the officers and we had to make a complaint. It took seven months before they actually took officers' statements," she told BBC Radio 4's Today programme.
Much of the progress in her brother's case was "down to the family" who had fought hard to help uncover evidence heard at the inquest, she added.
And she called for a fresh IPCC investigation, adding: "We very much welcome that as a family."
Ann Owers, chairwoman of the IPCC, said it would review the case and may reinvestigate.
"Obviously there is a lot more evidence, evidence that came out at inquest, evidence in Dr Casale's review.
"The first thing to do is to look at that and whether, on that basis, we need to look at our findings," she told Today.
She said the report had acknowledged improvements and "that we work with a very limited budget... often dealing with obstruction or reluctance on the part of the police".
In March, the IPCC arrested two serving and one retired police officers on suspicion of perverting the course of justice over evidence given at Mr Rigg's inquest. The officers remain on bail.
A separate independent review, partly prompted by Sean Rigg's death, recently called on the Metropolitan Police to improve how it deals with people with mental illness, saying they are too often treated like criminals.