Legal Question in Criminal Law in California

My guess is that they can search any part of the house that the ex-convict has access to.

good question, depends on whether it is a prole search, or if they have a warrant. But even if they can only search his room, if they see something in plain view in your house, they can take action.

The police will take great joy in tossing your entire house, and maybe they will also shoot your dog.