Quick answer
Refusal to sign does not necessarily prevent a divorce, but you must follow the applicable grounds, service, and court procedures.
Do now
Separate disagreement about ending the marriage from disagreements about money and children. Ask about contested procedures and lawful service. Keep evidence of attempts to obtain information through proper channels.
Watch for
Do not forge a signature, misstate an address, or assume silence means consent. A contested case can require financial disclosure and hearings even where no-fault grounds are available.
Official sources
NJ Courts — Divorce, NY Courts — Divorce frequently asked questions, DC Courts — Divorce.
