Do you cover third party liability if my pet bites somebody or causes a car accident by running across the street?

No, as most pet parents we surveyed didn’t find this benefit useful. Third-party insurance doesn’t cover incidents deemed to be caused by the owner’s lack of reasonable care, such as neglecting to use a leash or a muzzle when walking big or aggressive dogs. For feline owners, third-party liability is not much of a concern as cats are usually kept indoors and they rarely come into contact with others outside their homes.