Two of the robbers were killed along with a hostage who police said had been used as a human shield.
During the hour-long chase through the streets, two of the hostages jumped or were thrown from the stolen sport utility vehicle, one of them while it may have been going more than 50 mph (80 kph). At least one suffered a gunshot wound. Both were expected to survive.
It was not clear whether the hostage who died was shot by police or by the robbers.
The only surviving suspect was identified today as Jaime Ramos, 19. Police said the other robbers, ages 27 and 30, were gang members, also from Stockton.
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Police said that they recovered at least three handguns and an assault rifle and that the gunmen had ammunition strapped to their bodies.
At one point during the pursuit, the vehicle taken from a bank employee stopped around a corner and turned to face the direction officers were coming from, in what would have been an ambush, police said.
One of the gunmen was leaning out, taking aim with a rifle, police said. An officer shot at the gunman, and the SUV took off again.
When the SUV's tires were shot and the vehicle came to a stop, officers exchanged fire with at least one of the robbers, police said.
Jose Maldonado, who said he saw the robbers taking the women out of the bank, said the men had rifles slung over their shoulders and didn't seem to care that there were police all around.
"They were not afraid. They weren't going to take no for an answer. These poor women, they were screaming, they were so distraught, so scared," Maldonado said.