Adoption and change of ownership
The purpose of the move matters. California’s dog-CVI rule specifically covers sale, resale, adoption, and other changes of ownership or custody, so a breeder, rescue, shelter, or adopter should arrange the paperwork before pickup.
New World Screwworm rule
Companion animals arriving from a state with an active NWS infested zone currently require a premovement inspection within seven days, an electronic CVI with the required NWS statement, and a California entry permit.
Restricted species are different
California restricts some animals that may be kept as pets elsewhere, including ferrets, gerbils, hedgehogs, sugar gliders, and Quaker or monk parakeets. Contact California wildlife authorities before planning transport for a restricted or exotic species.