The criminal case belongs to the state
A DWI prosecution is brought by the state, and the prosecutor, not the injured person, decides whether to continue it. A victim's views may be heard, and a civil settlement can be part of what a prosecutor or judge considers, but neither the victim nor the driver can settle the criminal charge away. The word settlement is also used loosely for a negotiated plea, which is a separate discussion with the prosecutor and has its own limits in New York. Restitution ordered as part of a sentence is yet another item, and it can overlap with what an insurer pays. Keeping these strands apart prevents costly misunderstandings.
How the civil claim is usually handled
Claims for injury or damage from a crash usually run through your auto insurance, which generally has the right and duty to defend covered claims and to negotiate their settlement under the policy terms. In New York, no-fault coverage pays certain medical and wage losses regardless of fault, and larger injury claims proceed against the at-fault driver's liability coverage. Amounts above policy limits can create personal exposure, and punitive damages are often not covered by insurance. Reaching out to the injured person or the family to talk about money is a step to avoid, and so is signing anything they or their lawyer send without review. Report the claim to your insurer and forward any letters you receive.
Coordinating the two sides
In a first consultation we look at the criminal charges, the insurance policies involved, and whether a civil lawsuit has been filed or threatened. Statements made in the civil case can be used in the criminal one, so we coordinate with the lawyer your insurer assigns. We also discuss whether restitution or a voluntary payment through proper channels might be relevant at sentencing, and how to handle it without creating any appearance of pressure on a witness. Payments and offers are usually routed through the insurer, the lawyers, or the court rather than handed over in person.