Terry Smith, 33, died in hospital in November 2013, a day after being held in Surrey under the Mental Health Act.
He had been taken to Staines police station and kept in restraints.
The Independent Police Complaints Commission (IPCC) has referred the case to the Crown Prosecution Service.
The IPCC said two sergeants, one of whom had retired, and a health worker contracted to Surrey Police could face charges of gross negligence manslaughter and misconduct in public office.
It had investigated eight police officers and two staff,  the methods used to detain Mr Smith and why he was kept under restraint at the police station.
Police arrested Terry Smith, a father who lived locally, in Stanwell at about 22:00 GMT on 12 November 2013 after a call for assistance from an ambulance crew.
He fell ill and was taken to St Peter's hospital in Chertsey, where he died the following day.
IPCC Commissioner Jennifer Izekor said:  "We have now completed our investigation into the events leading up to Mr Smith's death.
"I have decided to refer the case to the CPS to determine whether any criminal charges should be brought against any officer.
"My thoughts remain with everyone affected by Mr Smith's death."
Charges of manslaughter and misconduct in public office are to be considered against three police workers following the death of a man restrained by officers.