You will be able to register this 1996 Toyota Camry in California without additional emissions components if its emission levels are low enough to pass the California Smog Inspection. HC, CO and NO emissions are measured.
Used vehicles being brought into California from out of state can pass the California smog test without needing any emission system modification or upgrades. So long as this Toyota Camry's original (federal) emission system have not been tampered with and the vehicle passes a smog test in California, it can be registered in CA.
We recommed you visit the website below to look up a 1996 Toyota Camry current emission cutscores for California. Compare the emission results of the previous emission test with the cutscore numbers.
California Emissions Cut Scores