Your insurance policy will likely specify what insurance your are required to have your tenants carry. This should be listed in the lease. There should also be language in the lease that specifies what the tenants policy covers and that you don't cover those things (damage to personal property, alternate accommodations under certain circumstances, etc).
You can't evict in CA if they tenant refuses to carry insurance.
The lease [here ](https://www.evict123.com/free-forms)contains good language regarding the consequences of not having renters insurance.