If your property borders a public area such as sidewalks, steps, driveways, parking spaces, and similar paved areas for public use, you are responsible for the upkeep of this area. This includes keeping the area free of all overhanging trees, shrubs, and other debris that block walkways, as well as keeping it from dangerous conditions. If any portion of a sidewalk or driveway is a danger to the public, the dangerous section must be repaired by the owner.
Ref LouisvilleKy.gov Codes & Regulations FYI: Who is Reponsible? Alleys, Right of Ways and Streets
Ref: Louisville Metro / Jefferson County Government Title XV (Property Maintenance Code) Chapter 156.052(C) (Exterior Property Areas - Sidewalks, driveways and yards)