It's true, there is a difference with California legal and Federal legal emission requirements. However your Toyota Corolla will pass the California smog inspection as long as it is equipped with the required Federal Emission Components, assuming it is in fact a 49-state emissions legal car. In other words, since presumably, it is an out-of-state vehicle, it is only required to be equipped with 49-state legal emission components, such as a federal and not California, CAT.
The only thing we ask that you make sure of is that your Toyota Corolla is in fact a 49-state emission equipped vehicle. You will need to check the "emission sticker" under the hood. It should state in fine print "49-State Emission Vehicle" or "49-State Federal Emission Equipped Vehicle".. something along these lines. It should not indicate anything regarding California. We only ask that you check this because simply having bought this car out-of-state is not a guarantee that it is an out of state vehicle. It may have very well been built for and emission equipped for California but at some point moved to Colorado and sold as a used vehicle. If this is the case, the vehicle will be a California emission equipped vehicle, and require a California approved CAT. Check the Underhood Emissions Sticker.