Police were called to Bulwell on Tuesday after receiving reports a man's behaviour was causing concern.
Witnesses told the Nottingham Post a man was seen "running out of a house naked" before damaging cars and houses.
He was arrested and taken to Queen's Medical Centre where he later died. The Independent Police Complaints Commission (IPCC) is investigating.
Nottinghamshire Police said they were called to Hoefield Crescent and arrested the man, but because of concerns for his health an ambulance was also called.
The IPCC said the man was declared dead shortly after arriving at hospital and it is now investigating the interaction between the man and officers.
His death is not believed to be suspicious.
IPCC Commissioner Derrick Campbell said: "It is important that we establish exactly what has happened and we would urge anyone who saw or heard anything that can help our investigation to contact us as soon as possible."
A man's death shortly after his arrest for going on a "naked rampage" is being investigated by the police watchdog.