If you can't find it, you will have to have to leave it blank, and print your return and file by mail. You will
write "refused" in the place for the SSN, and attach a written statement
describing the situation (you are separated but still married, she
refused, etc) and giving as much contact info for her as you can (name,
address, phone number).
In some cases it is possible to be
considered unmarried even if you are still married, but this is very
rare. You can be considered unmarried if you are "Legally separated from your spouse under a divorce or separate maintenance decree."
State law determines whether you are "Legally separated from your
spouse under a divorce or separate maintenance decree." In most states,
being legally separated does not count to be treated as single. For
example, in New York, separations are usually voluntary even if you file
papers with the court. A court order of legal separation is just as
expensive and complicated as a divorce, so no one ever gets one.
However, I do not know the rules of every state, so I can't say whether
you qualify. If you have a court ordered separation, you might contact
a tax attorney and see if you can file single too. Of course, if you
don't have a court ordered separation, you won't qualify. And if you
think you need to file as married, and file with the written statement,
the IRS will check out your wife's return and make a decision.
