Officers responded to an alarm at U.S. Bank at 39390 Fremont Blvd. at about 9:40 a.m., police Sgt. Chris Mazzone said.
Three men entered the banks with their faces covered. No weapons were seen, Mazzone said.
It is not yet clear how much money, if any, was taken, he said.
When police arrived they spotted a car leaving the scene. They chased the vehicle through Fremont, Union City, and into Hayward, where it crashed on Mission Boulevard near Industrial Parkway, Mazzone said.
Two of the suspects were apprehended at the scene of the crash while the third ran away.
Police chased the third suspect and, with the help of police dogs, found him in a garbage receptacle at about 11 a.m. and took him into custody, Mazzone said.