Your own claim: first-party disputes
When you claim benefits under your own policy, for property damage, disability, or similar coverage, a payment dispute is generally treated in New York as a contract matter. Courts have allowed consequential damages beyond the policy amount in some circumstances, when those damages were within what the parties contemplated, but New York does not generally recognize a separate tort for bad faith handling of a first-party claim. Punitive damages are rarely available and call for conduct well beyond an ordinary wrongful denial. Regulators can act on unfair claim practices, though that process is separate from recovering your own damages.
Claims against you: third-party bad faith
When someone sues you and your liability insurer controls the defense, the insurer has to give real weight to your interests in deciding whether to settle. If it turns down a reasonable chance to settle within your policy limits and a judgment then exceeds those limits, the insurer may be liable for the excess, although New York sets a demanding standard for proving that kind of bad faith. These cases often surface after a trial, and the insured sometimes assigns the claim to the injured party as part of resolving the judgment. Clear written communication about settlement demands within limits, with copies to you, can matter a great deal later.
Figuring out which situation you are in
Start with the policy, the claim correspondence, and any settlement demands or denials, along with their dates. If you are being defended under your policy and a settlement demand within limits has been made, it is worth having your own counsel review how the insurer responds. If your own claim was delayed or denied, the focus is usually the policy language, the quality of the investigation, and the deadline to sue. Our first job is to sort out which kind of bad faith question you have, what remedies are realistic in New York, and what should be done now to protect your position.