If your car is registered in California and it's newer than 1975, then you have to get a smog check every other year. If you change the engine, you're required to submit the vehicle to a State Smog Referee for inspection, which consists of a visual inspection and an emissions test. An engine change inspection can only be done at a state referee station.
My engine was from a 1990 C2. Nowhere on the paperwork do I see the engine number - it appears they took my word that the engine was a California-spec 1990 engine.
According to the docs I have from BAR, you do NOT have to run a cat, irrespective of the year engine you intall. This is because non-cat cars do not have a body design to accomodate the cat (or so one theory goes). From reading close, it would appear that the cat is considered part of the *car* and not part of the *engine*.
I have B&B headers on mine, and it didn't raise any questions at all. My custom ABS sewer pipe intake didn't raise any issues either, because there are no sensors in a stock airbox - they're in the air flow meter. I could use a pair of pantyhose for an air cleaner and it would be legal.
California BAR Engine Change Guidelines
Bosch DME manual pages I used to show 1990 C2/C4 engines to be exempt fro the "Check Engine" light
My paperwork from my failed first attempt at getting certified
My passing paperwork
This is the sticker you get when it's all said and done.