If you are moving to California from another state, you may register a 49-State Emissions legal vehicle if it was registered you in the state you are moving from. When registering your vehicle in California (in this case your Chevy Corvette), you must provide evidence that the vehicle was registered in your home state.
Health and Safety Codes 43150 through 43156 cover this requirement. H & S 43151 (c) covers out-of-state vehicles specifically.
43151. (a) No person who is a resident of, or who operates an established place of business within, this state shall import, deliver, purchase, rent, lease, acquire, or receive a new motor vehicle, new motor vehicle engine, or motor vehicle with a new motor vehicle engine for use, registration, or resale in this state unless such motor vehicle engine or motor vehicle has been certified pursuant to this chapter. No person shall attempt or assist in any such action. (b) This article shall not apply to a vehicle acquired by a resident of this state for the purpose of replacing a vehicle registered to such resident which was damaged or became inoperative beyond reasonable repair or was stolen while out of this state; provided that such replacement vehicle is acquired out of state at the time the previously owned vehicle was either damaged or became inoperative or was stolen. This article shall not apply to a vehicle transferred by inheritance, or by a decree of divorce, dissolution, or legal separation entered by a court of competent jurisdiction, or to any vehicle sold after the effective date of the amendments to this subdivision at the 1979-80 Regular Session of the Legislature if the vehicle was registered in this state before such effective date. (c) This chapter shall not apply to any motor vehicle having a certificate of conformity issued pursuant to the Clean Air Act (42 U.S.C. Sec. 7401 et seq.) and originally registered in another state by a resident of that state who subsequently establishes residence in this state and who, upon registration of the vehicle in this state, provides satisfactory evidence to the Department of Motor Vehicles of the previous residence and registration. This subdivision shall become operative 180 calendar days after the state board adopts regulations for the certification of new direct import vehicles pursuant to Section 43203.5. (d) "Established place of business," as used in this section, means a place actually occupied either continuously or at regular periods.