Regulation X does not require a signature on the HUD-1 form. Section 1024.9(a)(7) permits signature lines to be added to the form. The instructions for completing the HUD-1 are silent on signatures since the form does not require them. Box D on page 1 of the HUD-1 asks for the name and address of the borrower. If the spouse is not a borrower, then I would not think his/her name would go on the form.
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Opinions expressed are my own and not necessarily those of my employer. They are not legal advice.