See this link on the DMV site:
Click here for the DMV Link
Towards the bottom of the page, note this paragraph:
"Specially constructed passenger vehicles or pick-up trucks registered without a certificate of sequence are subject to emissions control requirements based on the model-year of the engine as determined by the Bureau of Automotive Repair (BAR) referee."
If being registered for the first time, you still have to go through the CHP (VIN), brake/light, and BAR inspection. If your engine is a 60's engine and you can prove it, make sure the engine meets the smog requirements for the year it was built. Then you should have no problems.
When I went to the DMV, I made a copy of their pertinent web pages. It helped tremendously as no one there appeared to know what to do. They made copies of the pages I printed from their own web site! LOL!
My situation was a bit easier since I purchase a used Cobra from NV that was already registered as a specially constructed vehicle in NV (2001 model year). The CA DMV changed it to 2004 and sent me to the BAR referee. All I need to do now is change out the carb and add the new air filter (which is not an easy task!)
Good Luck,
Howard