OAKLAND, Calif.  A day after four police officers were shot down in a rampage, the public and city officials struggled to understand how a routine traffic stop turned into one of the bloodiest days for police officers in California history.

“If we had a motive, we’d know why,” said Jeff Thomason, a spokesman for the Oakland Police Department. “And we want to know why.”

Mr. Thomason had no additional details about the investigations into the shootings on Saturday, which ended with the deaths of three officers: Sgt. Mark Dunakin, 40; Sgt. Ervin Romans, 43; and Sgt. Daniel Sakai, 35.

A fourth officer who was wounded in the shootout, John Hege, 41, was declared brain dead just before noon on Sunday at Highland Hospital, Mr. Thomason said. Officer Hege was being kept on life support as a potential organ donor.