Can my spouse stop a divorce in New Brunswick by refusing to sign?

This answer covers the law of New Brunswick.

No, your spouse cannot stop a divorce by refusing to sign. The ground for divorce is breakdown of the marriage, and nothing in the one-year separation rule makes the other spouse's signature or agreement a condition, so one spouse can petition and the court decides once the separation is proved.

Breakdown is established if you have lived separate and apart for at least one year before the divorce is decided. Spouses are deemed to have lived separate and apart for any period they lived apart, provided at least one intended to live separate, so the clock can run even in the same home, subject to proof. A reconciliation of not more than ninety days with reconciliation as its main purpose does not interrupt the period. Breakdown can also be shown without waiting where the other spouse committed adultery or treated you with physical or mental cruelty that makes continued cohabitation intolerable.

If your spouse agrees, you can file together on a Joint Petition (Form 72B); if not, one spouse files a Petition (Form 72A) and serves the other a Notice of Petition (72C). If your spouse disagrees, they can file an Answer (Form 72D), and the case continues to a judgment.