Bryson is facing possible felony hit-and-run charges over the first of the incidents, both of which occurred in southern California on Saturday evening, the Washington Post reported.
"Secretary Bryson was involved in a traffic accident in Los Angeles over the weekend. He suffered a seizure," CNN quoted his spokeswoman, Jennifer Friedman, as saying this morning.
"He was taken to the hospital for examination and remained overnight for observation. He was released and has returned to Washington. The investigation is ongoing."
According to a police statement, at around 5pm on Saturday, Bryson's Lexus rear-ended a Buick that was waiting at a railroad crossing in San Gabriel. He spoke to the three men in the other vehicle before driving off, hitting the car again on his way. Minutes later, Bryson allegedly collided with another vehicle in nearby Rosemead.
Police found him "alone and unconscious" at the wheel, the statement said. He was treated by paramedics and then taken to hospital with minor injuries. None of the other vehicles' occupants was seriously hurt.
Bryson was cited for felony hit-and-run while still in hospital, a spokesman for the San Gabriel Police Department told CNN. No charges have formally been filed.
The same officer told the Washington Post that Bryson would have been arrested and charged on Saturday, had he not been in hospital. As it is, he was instructed to appear at Alhambra Superior Court in 60 days.
At this stage there is no reason to believe that drugs or alcohol were involved, police said.