It would depend on the terms of any applicable policy and the facts asserted. If I were representing a landlord, I would certainly tender defense of any claim to the landlord's carrier.
The answer is: it depends. Residential and commercial policies universally contain terms which would exclude coverage for claims based upon mere habitability, especially those that relate to failure to repair and maintain the premises, which have not resulted in any non-economic injury.
However, the duty to defend is broader than the duty to indemnify. There are many claims that could be made against an owner of real property which may relate to habitability which not only required defense by the carrier but also indemnification.
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The insurance carrier's duty to defend depends upon a number of factors, most importanly, the terms of the policy and the claims being asserted. If the tenant's complaint alleges a cause of action for negligence causing bodily injury to the tenant, most likely, the insurance carrier would have the duty to defend and indemnify. If the tenant's complaint only includes causes of action for breach of contract or causes of action for intentional torts, the insurance carrier would not have a duty to defend.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This Avvo.com posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult with your own attorney.