I know that no one is required to carry identification in California, so long as the person isn't driving or in a secured area like an airport.
Now if police have "reasonable suspicion" to stop someone, but lack probable cause, and the person refuses to show ID and to answer any question at all, including to identify oneself by name, certain attorneys here have said that police can detain someone for a reasonable amount of time to determine their identification.
Some attorneys went so far to say that police may compel the person to give a fingerprint in the field (i.e., in public, on the street) or even arrest and take the person to the police station pending identification.
Simply refusing to cooperate creates probable cause to arrest, or allows them to compel fingerprinting???