A landlord can be liable for a tenant's injuries caused by a leaky roof in the rental property if the landlord knew or should have known that the roof was leaking and that it created a dangerous condition. This was the ruling recently by the Kentucky Court of Appeals in Warren v Winkle, No 2012-366 (May 24, 2013).
This ruling does not mean that a landlord will always be liable for a tenant's injuries caused by a leaky roof; the landlord's conduct and liability will be always be subject to a reasonableness test. Liability for the landlord will have to be assessed on a case-by-case basis.
There is a discussion of this case by Robert Abell at Abell's Kentucky Law Blog: Landlord Can Be Liable for Tenant's Injuries Caused By Leaky Roof, Kentucky Court of Appeals Rules.
Contact Lexington personal injury lawyer Robert Abell at 859-254-7076.