Police want anyone who was near Etihad Stadium about 3pm on Monday to contact them after a confrontation with officers outside the sports complex that led to a shooting.
An officer shot a man, 34, and he is under police guard in hospital.
Investigators believe several people were walking and in cars nearby at the time, but left before they spoke to police, a spokeswoman said.
Anyone who did not contact police is asked to phone Crime Stoppers on 1800 333 000.
Two other men have been charged with burglary.
A Southbank man, 24, and a Docklands man, 23, have been bailed to appear at the Melbourne Magistrates Court next year after they were arrested outside the stadium.
Commander Rick Nugent said four plain-clothed police officers investigating car theft located a stolen vehicle in the car park off Bourke Street about 3pm.
When a man walked up to one of the stolen cars, a policeman produced identification and spoke to the man.
The man allegedly then pulled a pistol from the front of his pants and threatened the officer, who ran for cover, chased by the man. Another police officer then shot the man.
Commander Nugent said it did not appear that the man fired any shots. He also said he did not know whether the man was known to police before the shooting, where he was shot, or how many times he was shot.
When the shooting occurred, the police were conducting an ongoing investigation into car theft in the Melbourne area, Commander Nugent said.
He said it appeared at first glance that the policeman who shot the man had acted appropriately.
’’Based on the briefing I’ve been given, the members were threatened by a male with a firearm, they had to resort to the use of a firearm. That’s what we have at the present,’’ he said.
’’However, like all police shootings, it will be thoroughly investigated independently.’’
The man recovering in hospital will be questioned by police. He has not been charged.
Police said the 24-year-old Southbank man was charged with two counts of burglary, two counts of theft and theft of a motor car.
The 23-year-old Docklands was charged with two counts of burglary.
Both were bailed to appear at the Melbourne Magistrates Court on April 30.
With Adrian Lowe