In box 3 of Form W-4, there are three boxes for filing status: Single, Married, and Married but withhold at higher Single rate.
You should check Single if you are single, divorced or separated under a court decree of separate maintenance. You should also check single if you are married but your spouse is not a citizen or resident of the United States. You would not normally be able to file a joint return. But if one of you is a U.S. citizen or resident, you can choose to treat the nonresident spouse as a resident for tax purposes. In this case, you would be able to file a joint return and could check the Married box on Form W-4.
You should check the Married box if you are married and neither you or your spouse is a nonresident alien. You are considered married for the year if you are married on the last day of the year. You are also considered married for the whole year if your spouse died during the year. You should also check the Married box if you expect to be able to file as a qualifying widow(er) with dependent child. You may be able to claim this status for 2 years after your spouse died. By December 1 of the last year you can file as a qualifying widow(er) you should file a new W-4, showing your status as Single for the following year.
You should check the Married but withhold at a higher Single rate if you are married but you find that not enough income tax is being withheld to cover your tax liability. This may happen, for instance, when both spouses work. In this case, you may want to fill out the Two-Earner/Two-Job Worksheet, which is explained below.