A woman was injured and emergency services were called to the intersection of King and Pitt Streets in Sydney's CBD about 9pm on Thursday following reports of a carjacking.
Police were told a 36-year-old man stole a Mazda sedan from its driver, a 26-year-old woman, before driving off along George St.
The Mazda collided with a rideshare vehicle at the intersection of Market Street, and then crashed into a nearby police car.
A male driver, 27, and female passenger, 24, were inside the rideshare vehicle.
The Mazda then struck a bollard, which dislodged and struck a 58-year-old female pedestrian.
The woman, who had been shopping nearby, was treated by paramedics for a cut to her head before being taken to hospital in a stable condition.
Officers from inside the police car which had earlier been struck then arrested the 36-year-old man at the scene.
Footage from the scene showed the alleged offender dressed in his underwear and apparently covered with blood.
A large crowd watched on as he was attended to by officers.
NSW Police Acting Superintendent Adam Solah said it was fortunate no one else had been injured.
"It was definitely a chaotic scene," he told reporters on Friday.
"A number of bystanders came in to offer medical assistance to everyone who was involved, and they did a really good job in doing that."
Act Supt Solah also praised the efforts of police who rushed to make the arrest despite their vehicle being struck moments earlier.
"They were able to get out of the vehicle straight away and arrest that male person," he said.
"They did an excellent job of that ... it would have been quite a shock for them to see what had occurred. "
He described the alleged carjacking as a "completely random attack," adding the man was not known to the original driver of the Mazda.
Act Supt Solah said the man was also not known to NSW Police, but was familiar to their South Australian counterparts.
Following his arrest, the 36-year-old was taken to St Vincent's Hospital for mandatory testing under police guard, where he remains.
He was charged with assault with intent to take/drive motor vehicle, negligent driving with no death or grievous bodily harm, common assault, and destroying or damaging property.
He was refused bail and is due to appear at Downing Centre Local Court on Wednesday.
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