One man has since been questioned on suspicion of causing grievous bodily harm.
Police were called to Market Street in Ashby-de-la-Zouch, Leicestershire, at 10pm on Thursday.
They had received reports that two men had entered a store and demanded cash, threatening staff at a Co-op store with a golf club and baseball bat.
One of the suspects got away in a waiting vehicle, but Shane Bryant, 29, was held in the street near the store until officers arrived.
He died in hospital in Nottingham on Saturday after being taken ill at the scene.
Leicestershire Police said “a 24-year-old man was arrested on suspicion of grievous bodily harm to allow officers to carry out a prompt and balanced investigation”.
The force added: “He has since been released from police custody pending further investigation.”
Detective Chief Inspector Di Coulson said: “We are keen to have any dashcam and mobile phone footage that anyone may have of the incident on Thursday night.
“There were lots of people in the area who saw what happened and were involved in apprehending Mr Bryant.
“No matter how short or insignificant you think it is, we would like to see it please.”
A friend of Mr Bryant, Serina Larvin, has set up a fundraising page, saying: “A much loved friend of our community got taken away in unexpected circumstances.
“He left behind two small children and a absolutely heartbroken family.
“I thought it would be nice to raise some money to give to his children and help support the family in any way possible.”
A separate investigation is also being carried out by the Independent Police Complaints Commission into officers’ contact with Mr Bryant.