You were 'Jointly and severally' liable to pay the tax (i.e either of you could have been persued to pay the whole debt), wouldn't you be also jointly and severally due the refund also? The refund is surely due to either or both of you. You'd need to research it further and find out.
difficulty is you've already lied, perhaps you would be perfectly correct to claim the full refund yourself.
find out whether you alone can claim the refund, if you can, see if you can backtrack. At the moment you've only said she lives there and been sent the paperwork accordingly. Thats just a mistake, but maybe its a mistake they made, it was a bad line and you said 'no' but they heard 'yes'.
You knowingly signing the paperwork turns the mistake into fraud though.
If you can legitimately claim the refund yourself (because although two of you were named on the bill perhaps only one of you might have been funding the payments) call them and tell them you've been sent the wrong form to fill in 'by mistake'.