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You should never sign anyone else's name, especially if they have not authorized you to do so. If your wife refuses to file a joint tax return with you, consider filing separate returns. You should consult your own attorney and tax advisors.
No . If you sign the name if would be a crime. Don't do it, not worth it and she will find out.
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Signing another's name on a Treasury check probably is a violation of several Federal laws. You can return the check to the Treasury department, but it would make a lot more sense to work out something with your wife.