Sheku Bayoh, 31, was detained by police during yesterday’s incident in Kirkcaldy, Fife.
He died a short time later in custody.
The Police Investigations and Review Commissioner (PIRC), set up to investigate serious incidents involving the police, is leading an inquiry into the matter.
A PIRC spokeswoman said: “The Crown Office and Procurator Fiscal Service (COPFS) has directed the Police Investigations & Review Commissioner (PIRC) to carry out an independent investigation into the circumstances surrounding the death of 31-year-old Sheku Ahmed Tejan Bayoh in Kirkcaldy on Sunday 3 May who had been detained by police shortly before his death.
“A report on the PIRC’s findings will be submitted to the COPFS in due course. As this is a live investigation it would be inappropriate to comment further at this time.”
Police Scotland previously confirmed that a female police officer was injured during the incident, but gave no further details.
Fife Divisional Commander Chief Superintendent Garry McEwan said earlier: “This is a tragic set of circumstances and my condolences go to the man’s family.
“The investigation of deaths in Scotland is the responsibility of Crown Office and Procurator Fiscal Service, who have instructed the Police Investigations and Review Commissioner to lead on this inquiry.”