Church caretaker Thomas Orchard, 32, died on 10 October last year in hospital, seven days after his arrest in the city centre.
The police watchdog confirmed it has now asked prosecutors to consider charging four police officers, two custody staff and an agency nurse.
The Devon and Cornwall force declined to comment on the investigation.
Mr Orchard, a caretaker at St Thomas Church in Exeter, was arrested on the morning of 3 October on suspicion of a public order offence, according to the file from the Independent Police Complaints Commission.
'Quiet and devout'
Just over an hour later Mr Orchard was taken by ambulance to the Royal Devon and Exeter Hospital as he was “unresponsive in his cell”.
IPCC commissioner Rachel Cerfontyne said: “It will be a matter for the Crown Prosecution Service to determine whether criminal charges will be brought against any of those police staff involved in Mr Orchard's detention on that day.”
The force said the four officers and two staff had been placed on “restricted duties”, despite calls by the IPCC for them to be suspended.
The force said in a statement: “We would not comment on the investigation or status of the officers other than to say they remain on restricted duties.”
The Reverend Ann Dowdeswell of St Thomas Church said Mr Orchard, who had been employed at the church for at least a year, “was a really important and valuable member of our staff”.
She said: “He was quiet and devout.
“He joined the church as a member of the congregation and is sorely missed by everyone.”
