It's actually more complicated than that. Each species has some sort of state, county and city regulations (and of course federal regulations). Technically in CA, you can capture one or two native rattle snakes yourself and keep it in your possesion without the proper license or permit. However, the county of Los Angeles overall prohibit that. But there are some cities within Los Angeles that allows it. In San Bernardino, overall they are okay with capturing and keeping native rattle snakes in your possesn and few cities within San Bernardino that completely ban them. A very vague and general rule of thumb is the more civilized/populated the city/area is, the more likely they will ban keeping venomous species; the more rural the area is, the more likely the city/area will be lenient towards having them in your possession. Note that these laws state that the person in possession actually captures these native species themselves. Buying them requires special permits that usually researchers and educators can only get. I only know the laws and regulations concerning the rattle snake species because two of my friends personally have rattle snakes as pets and I was interested in getting one (I know, stupid idea), but the whole capturing it yourself pretty much killed that plan thankfully. Also if you want to keep more than two specimens of rattle snakes, you have to get 2 documents. One document (permit or license) to actually go out in the field to acquire the animals and take them out of their natural habitat. Another document (license or permit) to keep them in your possession.
I don't know the rules and regulations of that particular species, Heloderma horridum, but I would check with your local county and city regulations. Also if you live in a place with a HOA, you might want to keep that animal your personal secret.
I do believe a fishing license is required to catch reptiles in California...go figure on that one ehh...