The man fell from the car park of the Utilita Arena - what was the National Indoor Arena - after police were called to reports of a man breaking into cars in the early hours of Tuesday morning.
He has now been dearrested, West Midlands Police has confirmed.
According to the College of Policing, a person should be de-arrested when the grounds for arrest cease to exist, further information comes to light indicating they are not responsible for the offence, or when the potential breach of the peace has ended.
It is believed the man was attempted to jump to a lower floor in the North Car Park on King Edwards Road in Birmingham as officers tried to restrain him when he fell.
The man remained in hospital with a broken ankle, broken pelvis and back injuries on Wednesday.
A spokesman for West Midlands Police said: "We were called to a car park at the NIA on King Edwards Road just after 2.30am to reports that a man had been breaking into cars.
"A suspect was identified but tried to jump to a lower floor as officers tried to restrain him. The men then fell around 40ft onto the pavement below.
"Our professional standards department is investigating and the matter will be referred to the IOPC, as is routine in the circumstances."
Part of the car park had to be cordoned off by police throughout Tuesday morning as a result.