Dorset Police said officers had restrained the man, who was reported acting erratically in Poole on Tuesday.
The man suffered a medical episode while with the officers, who performed CPR while waiting for an ambulance.
He was taken to Poole Hospital but his condition deteriorated and he died on Wednesday morning, police said. His next of kin have been told.
Police have referred the death to the Independent Police Complaints Commission (IPCC).
A statement from the force said officers were called at 16:12 and 16:19 BST amid concern for the man's welfare.
The statement said: "When officers arrived, a man matching the description was found on The Avenue. He was restrained while officers assessed the situation.
"While with officers he suffered a medical emergency. The ambulance service was requested to attend and officers performed CPR while awaiting their arrival.
"The man was taken to Poole Hospital for further treatment. Sadly, his condition deteriorated and he died in hospital this morning."

Sixty teams submitted plans for Clandon Park House in Surrey, which was reduced to a charred shell in 2015.
The National Trust has announced a shortlist of six teams, as well as the names of those on the jury, which will make a final decision after a public consultation over the summer.
Building work is expected to begin by early 2019, the National Trust said.
The National Trust said it wanted plans to combine restoring state rooms in the Grade I-listed building with new galleries and visitor spaces.
Sandy Nairne, who is chairman of the jury, said: "We received an excellent set of submissions, offering many fascinating collaborations and partnerships.
"The shortlist represents a collection of great talent from the UK and abroad.
"The teams that were selected had thoroughly analysed the conservation issues and design opportunities, and proposed thoughtful and creative approaches."
The six shortlisted teams will create concept designs which will go on public display in the late summer, The winning team is due to be announced in early autumn, the National Trust said.
The trust said the high-profile project had a Â£30m construction value.

Almost one million people have been evacuated from coastal areas in anticipation of a typhoon carrying wind speeds of 173km/h (107mph). Some 100mm of rain has fallen since Friday.
Chan-hom is now heading north past the city of Shanghai.
The typhoon hit Taiwan and Japan earlier in the week, uprooting trees and injuring several people.
Chan-hom first hit Zhejiang province on an island near the city of Ningbo at around 16:40 (08:40 GMT), the National Meteorological Center said.
No deaths or injuries were reported in the region by Saturday evening, state news agency Xinhua said.
One village, Laiao, received more than 400mm (16in) of rain, it said.
The BBC's John Sudworth in Shanghai says more than 400 flights have been cancelled there along with a number of public events, and the government has told people they should stay at home.
Dozens of flights were also cancelled in Zhoushan, Hangzhou, Ningbo and Wenzhou.
Zhejiang province has called its entire fishing fleet back to port.
Some 100 train services were also cancelled.
Peter Abram, who is in Ningbo, told the BBC: "The supermarkets got cleaned out yesterday morning. I just tried to take a walk, but got blown back inside.
"The only people out in the thick of it are emergency services... All us Westerners here in Ningbo seem to be safely battened down in our apartments, candles at the ready."
Philippa Osborne, who is in Shanghai, said: "From where I live in the middle of Shanghai, people have certainly heeded the warning to stay home. There are virtually no pedestrians out on the street, and the road traffic volume has been greatly reduced."
Chinese television showed footage of coastal regions being battered by torrential rain as the typhoon neared.
Images from the region also showed flooded farmland.
Our correspondent says China is well used to dealing with such storms, although this is possibly the strongest July typhoon to hit Zhejiang since 1949.
The highest red-alert warning remains in force, despite the storm being downgraded in category from super to strong.
A man who police had been called to help after he was seen wandering among traffic has died in hospital.
[NEXT_CONCEPT]
The National Trust has announced the design teams shortlisted to rebuild an 18th Century mansion destroyed by fire.
[NEXT_CONCEPT]
Powerful typhoon Chan-hom has made landfall along the coast of China's eastern Zhejiang province.