Ruling was based on the vagueness of "credible and reliable" identification in California law.
Justice Brennan, in his concurrence, does states "Even if the defect identified by the Court were cured, I would hold that this statute violates the Fourth Amendment....States may not authorize the arrest and criminal prosecution of an individual for failing to produce identification or further information on demand by a police officer."
The SC in Hiibel did rule that identifying yourself does not violate 4th and 5th Amendment.