Impact of No-Fault Grounds
Before 2010, your only options in New York were to file for divorce on fault grounds or negotiate a separation agreement with your wife. You'd then have to wait two years, living apart the entire time, before you could divorce. Since 2010, however, you can file on grounds that your marriage is irretrievably broken. Your wife can deny the grounds, but if the two of you disagree on such a fundamental issue and you want to end the marriage, it's obviously broken. The court will honor your grounds if you state so under oath. If you use any of New York's fault grounds instead, such as adultery or cruel treatment, you'll have to prove to the court that these instances of marital misconduct occurred – and your wife could try to prove otherwise.
New York's Rules for Service
After you file for divorce, you must serve your wife with a copy of your complaint and an Affidavit of Defendant. If you suspect she won't accept the papers, you can hire a professional process server to deliver them to her. Ideally, your wife would sign the affidavit, acknowledging receipt of your divorce complaint. If she doesn't want the divorce, however, she can refuse to sign. If this occurs, the process server can complete an Affidavit of Service, attesting that he gave her the papers, and you can file this with the court instead to prove service. If the server can't find her to give her your paperwork, you can file an Affidavit of Attempted Service with the court and let a judge know that your wife is dodging service. The judge will authorize service in some other way, such as by publishing a notice in the newspaper, so your divorce can proceed.
Divorce by Default
After you've managed to serve your wife with your complaint, she has 20 days to respond under New York law. If she refuses to do so, this hurts her, not you. Forty days after her deadline expires, you can ask the court to grant your divorce by default, without her cooperation. The court will grant your request because your wife has not filed an answer to your complaint to indicate she wants to take part in the divorce proceedings. In all likelihood, you'll receive whatever you asked for in your complaint because she hasn't objected.
Contesting the Divorce
Your wife can significantly complicate your divorce if she files an answer to your complaint within the allotted time. If she does this, she's contesting your divorce. She may not be able to dispute your grounds if you use the no-fault option, but she can force you to litigate all other issues, such as property division, support and custody. This won't stop you from getting your divorce, but it will force you to go to trial so a judge can resolve these issues. At best, your wife might be able to delay your divorce for a while, but eventually, you'll get it.