Legal Question in Real Estate Law in California

Yes, unless there is a rent control ordinance to the contrary in your location.

I guess it depends upon what you mean by "require." The landlord can certainly ask for them. The landlord can also take into account your refusal to furnish them in making his/her/its decision whether to rent to you or not. However, unlike someone lawfully issuing subpoenas, the landlord lacks the power to compel you to furnish them.