In a recent decision, the Kentucky Supreme Court has interpreted Kentucky statutes as permitting a landlord to be held liable for their tenants' dogs if they attack someone on or about their property. Benningfield v Zinsmeister, 2009-SC-000660-DG(6/25/12). The Court determined that a landlord can be considered the statutory owner of the dog if the landlord allowed the dog to be kept on the leased premises. This opinion was a plurality opinion meaning it is not necessarily binding precedent on future courts and is not yet a final opinion.
Although it does not appear that the law in Kentucky is well settled on this issue, landlords will assuredly be unhappy about this ruling fearing an increase in their insurance premiums. Of course, the landlords can protect themselves by choosing not to rent to dog owners, requiring an additional animal fee as part of rent to help offset the increased premiums and/or require renters to carry renter's insurance as a condition to renting the property.