There is a difference with California legal and Federal legal emission requirements. However if this Chevy Cougar is equipped with the Federal required emission components (which it originally came with) it can pass the California smog check and register with the CA DMV.
The rule is any USED vehicle which is equipped with the necessary Federal Emission Components is eligible for California registration as long as the vehicle's exhaust emissions fall within California's limits and the vehicle's emission system has not been tampered with. This exemption does not apply to new vehicles.
The emissions inspection for late model vehicle are similar for late model vehicles in both California and Arizona. For the purposes of title transfer and sales, it is recommend that you have an Arizona title in your name prior to registering or selling the vehicle in California. Without a title in your name, you may have difficulty proving the chain of ownership when attempting to sell the vehicle here.