The 2010 hires were prompted by a consolidation aimed at saving money.
Supervisor Mike Antonovich, who made the motion for the investigation, said that the board was promised at the time that only those officers who met Sheriff's Department standards would be hired.
"We ought to know who made these exceptions to the rule," he said. "We need to hold those people responsible."
The hiring was prompted by the Sheriff's Department taking over patrols of parks and government buildings from the Office of Public Safety. Officers there were given first shot at the new openings in the Sheriff's Department.
Of the 280 who were hired, the Times found that background investigators knew that 188 had been rejected by other law enforcement agencies, 92 had been disciplined by other agencies for significant misconduct on duty, and 29 had been fired or pressured to resign from a previous law enforcement job.
The Board of Supervisors on Tuesday unanimously approved the motion, which calls for a report from Baca in two weeks.