California Code, Health and Safety Code - HSC § 43654

(a) Except as otherwise provided in subdivision (b), every 1966 through 1970 light-duty motor vehicle, subject to registration in this state, shall be equipped with a certified device to control its exhaust emission of oxides of nitrogen upon initial registration, upon transfer of ownership and registration, and upon registration of a motor vehicle previously registered outside this state.

(b) Subdivision (a) shall not apply to a 1966 through 1970 light-duty motor vehicle (1) which is registered to, or subject to registration by, an elderly low-income person, (2) which was purchased from a person other than a dealer or a person holding a retail seller's permit, and (3) which is used principally by or for the benefit of the elderly low-income person. However, only one vehicle described above shall be registered to, or subject to registration by, the elderly low-income person at any one time.

(c) For purposes of subdivision (b), the Department of Motor Vehicles may require satisfactory proof (1) of the age of the transferee of the motor vehicle, (2) of the combined adjusted gross income of the household in which the transferee resides, and (3) that the transferor of the motor vehicle is a person other than a dealer or a person holding a retail seller's permit.