If you can't find it, you will have to have to leave it blank, and see if it will let you print your return and file by mail. You can 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.
