For a long time, certain dogs and insurance companies have been at odds. Carriers have had lists of "bad dogs" dogs of particular breeds that they would not provide a homeowner's policy for because of the risk of injury caused to others by the dogs. Various cities had restrictions on dog breeds as well.

Thinking has changed over time, and many states now no longer have restrictions by dog breed, only the behavior of the dog. Many have statutory definitions of "dangerous dogs" and once a dog has met that definition, certain liability insurance is required. See Dog Bite Statutes Part II – Definition of "Dangerous" and Dog Bite Statutes Part I – Liability Laws.

Recently the Governor of New York signed legislation prohibiting insurers from refusing to issue or renew, cancel or charge an increased premium for a policy based solely on the harboring or owning of any dog of a specific breed or mix of breeds. Once a dog meets the definition of dangerous dog, an insurer can then decline, nonrenew, cancel, or increase premium because of an insured owning that particular animal. A copy of S4254 can be found here.