When you are suing the insurer
A suit against an insurance company usually begins as a breach of contract claim based on the policy. Many policies contain their own deadline for bringing suit, which can be shorter than the general limitations period, along with appraisal or proof-of-loss provisions that have to be handled correctly. New York is generally more limited than some states in allowing a separate bad-faith tort claim when your own insurer denies coverage, although consequential damages can sometimes be recovered within a contract claim, and a liability insurer's handling of a settlement offer within policy limits follows different rules. You can also complain to the New York Department of Financial Services while a lawsuit is pending, but that complaint does not replace a suit or pause its deadlines.
When the insurer sues you
Insurers sometimes file a declaratory judgment action asking a court to rule that a policy does not cover a claim, or that the policy should be rescinded because of a misstatement in the application. These cases often arise while you are being sued by someone else, and the insurer may be defending you under a reservation of rights at the same time. That combination raises real questions about who controls the defense and whether you are entitled to independent counsel. Respond to the complaint on time, notify any other insurers that might cover the loss, and do not assume the defense lawyer the insurer appointed in the underlying case is advising you on coverage.
The file behind most of these cases
Gather the complete policy, including declarations, endorsements, and the application, because coverage often turns on an endorsement nobody read. Collect all correspondence with the insurer and its adjusters, the denial or reservation of rights letters, and your proof-of-loss submissions. Keep records of the loss itself, such as photographs, repair estimates, and invoices. In a first meeting we read the denial against the policy language, check the suit limitation and notice provisions, and talk about whether negotiation, appraisal, or litigation fits the dispute. Insurance disputes often narrow quickly once both sides are working from the same complete policy.