Most homeowners’ policies specifically exclude criminal acts and intentional acts. So, the insurance company would likely assert that it is not responsible.
Whether the insurance company prevails in that situation would really depend on the facts of the case. For example, if the insurance company insures your Rottweiler and it bites three people in 2015, and they settle those claims, and subsequently in 2016, your Rottweiler bites two more people, while it remained as a covered animal on the policy, ti would be difficult for the insurance company to slide out to avoid responsibility. In that situation, it certainly appears that the insurance company has taken a knowing and voluntary risk of insuring a dangerous animal.
Learn more about dog bites in California.