CHP spokeswoman Fran Clader said there were at least four confirmed deaths by early evening, but she had no details. Five hospitals were treating the victims.
Clader said authorities believe 36 people were on the vehicle, but they had not yet received a passenger manifest to confirm that.
The maroon bus, bearing the name Orion Pacific, lay on its side after crashing into the guard rail on the two-lane southbound overpass. Luggage and clothing was strewn on the road.
A person who answered the phone at Orion Pacific, which describes itself as a luxury charter coach company based in Orange, said no one was available for comment. It was not immediately clear who had chartered the bus.
Jacques de Noray, a spokesman for the French consulate in San Francisco, said authorities notified his office that there were some French citizens involved in the crash.
Clader could not comment on Orion Pacific's safety record pending the accident investigation.
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