If you filed as married filing joint then the answer is almost certainly yes, they can withhold the refund - provided the school has followed the proper procedure to report the unpaid debt to the state tax agency - because as a joint refund the money belongs to both of you. However, you may be able to get back the portion that belongs to you based on your relative taxable incomes and tax liabilities (figured as if you had filed separately); you will have to check with the contact information on the notice you received to see if there are any procedures you can follow or forms you can file to get back at least part of your refund.
My answer does not constitute legal advice and may not be relied upon by anyone for any purpose and does not constitute an attorney/client relationship or an offer to form such a relationship. This disclaimer is intended to be fully compliant with the requirements of Treasury Department Circular 230 and the terms thereof are fully incorporated by reference. If you wish to consult with me please contact me at dana@nytaxcounsel or visit my website at www.nytaxcounsel.com