Although it was an additional insured under the tenant's commercial general liability policy, the landlord was not entitled to a defense for injury arising out of property other than the leased property. See VBH Luxury, Inc. v. 940 Madison Assoc. LLC, 2012 N.Y. LEXIS 217 (N.Y. Feb. 14, 2012).
The landlord was an additional insured "only with respect to liability arising out of the ownership, maintenance or use of that part of the premises leased to tenant." Therefore, the landlord would be entitled to a defense in an action against it by a third party for an injury suffered on the leased premises.
The policy, however, did not provide coverage for liability to the landlord for damage to property owned, rented, or occupied by the tenant. Therefore, the insurer was not obligated to defend the landlord in the underlying action.