Twice the police had tried to stop and check on a car, which kept getting away. Shortly after 2 pm it disappeared again from the scene, driving fast southwards on Amiralsgatan. The next time police see the car, it has smashed into three parked cars, one of which was thrown up onto the pavement.
A witness to the accident told the tabloid Kvällsposten online that car was chucked "seven, eight metres into the air" and landed on the pavement.
The three injured people seem to have been on the pavement at the time. Two of them, a woman in her thirties and a child, have suffered life-threatening injures, and the third, also a woman, is seriously injured, according to newsagency TT.
Three men in their early twenties have been arrested by the police, for alleged involvement in the accident. Police suspect the driver may have been on drugs.
An internal investigation will now try to establish the speed of the police car, and whether the way the car chase was carried out could have contributed to the accident, Swedish Radio News reports.
But traffic researcher Jörgen Lundälv at Umeå University, who has carried out research into emergency services and driving, tells the news agency TT that it is far too dangerous to start a car chase in a heavily populated area.
"To carry out a car chase in the central parts of an inner city is completely reprehensible. The risks are far to big," he tells TT.
"So if the police car had caught up, how would they have stopped them? The police are only allowed to stop and force another car to stop when it is safe, with low traffic intensity and there is no risk to a third party. What plan was there here?" he asks.