When I imported my '61 truck from Arizona to California I had to do a few things including a cursory physical inspection at the DMV, and I had to get the truck weighed and provide a certified form stating the weight. I get charged extra on my registration each year because it's apparently considered "Heavy" (4995 lbs.). It weighs the same as my wife's Land Cruiser, FWIW. The physical inspection consisted of them checking the VIN plate on the frame inside the driver's side door, checking the headlights and tail lights. This was ~6 years ago, and the rules may have changed. Anything pre-1975 is smog exempt, but if you have any obvious modifications that are not street legal, the DMV inspector will probably catch them.
