Legal Question in Criminal Law in California

Not necessarily. If the officer genuinely believed at the time that the car was not registered, then saying so is not perjury even if his belief was mistaken. I can think of other scenarios in which he would not be perjuring himself.

Not necessarily. Perjury is knowingly offering false testimony under oath. If he just believed the car was unregistered (for example if he thought the registration was expired, but the stickers just hadn't been put on the plate ), that's not perjury. On the other hand, if he ran the plates and it was registered - and he knew that at the time - but testified he didn't know that, that's a lie and potential perjury.

Another situation I can think of is when the officer runs the car and the database contains an error. The officer relied on that error, and that is also not perjury.