Not being from California I can't say for certain, but I will tell you what is the common rule in most, if not all, states. A landlord is obliged by health codes to reasonably keep a property a healthy place to live and this entails general extermination for such as reaches, bedbugs, and other common pest. He/she can however, if they have just cause to believe the tenant is the source of the infestation, charge or even evicted that tenant. I would suggest that you call a real estate agent or an attorney specializing in reality to make certain of the laws in your area.
Some of the pests or insects that the California government housing landlords are required to exterminate include bedbugs and other related vermin. Landlords in almost all the states in the US are required to keep their rental premises or properties more habitable. Check out http://www.ehow.com/about_6374829_tenants-rights-pest-control.html for more information.