Two words, two systems
In the traditional civil sense, assault is putting someone in reasonable fear of an imminent harmful or offensive contact, and battery is the contact itself. Many states keep a version of that split in their criminal codes, often with battery covering unwanted or harmful touching. New York's Penal Law does not. Criminal assault there generally requires a physical injury, and unwanted contact without injury is usually treated as harassment. New York civil law, though, still recognizes assault and battery claims in the traditional sense, so the same words can mean one thing in a lawsuit and something else in a criminal courtroom.
When a lawsuit runs beside the criminal case
A person who was hurt can bring a civil claim for damages separately from any prosecution, and the two follow different rules, proof standards, and deadlines. A civil claim can continue even if the criminal case is dismissed. What you say in one can be used in the other, so testimony at a deposition or a statement to an insurer should be coordinated with your criminal defense lawyer. Homeowner's and renter's policies often exclude intentional acts, which affects whether an insurer will defend you, but read the notice terms in any policy early. For someone who was injured, the time limit for an assault and battery claim in New York is shorter than for many other injury claims, and claims involving a public employer can carry an even shorter notice requirement.
Sorting out which case you are in
We start by identifying what exists: a criminal charge, a civil complaint or demand letter, an insurance claim, or several of these at once. We confirm which state's law applies, since that changes the terms being used, and we look at the deadlines in each proceeding. We then talk through how decisions in one case could affect the other, including whether and when to give any statement. Bring every paper you have received, including envelopes that show dates of service.