They have the ability to. Whether or not they will is probably dependent on your situation. Here's some more information:
From Minnesota's Department of Revenue site:
The Revenue Recapture Act authorizes the Minnesota Department of
Revenue to intercept (or “recapture”) your tax refunds to pay debts you
owe to other state and public agencies, including the Minnesota college
and university system, certain local governments, or the IRS.
Revenue recaptures only apply to individual tax refunds or other
payments. The law doesn’t apply to corporations or corporate tax
returns. Debts subject to recapture include, but are not limited to:
claims for child support, medical bills, student loans, traffic fines
and federal taxes.
In addition to income or property tax refunds, the department may
recapture lottery winnings of more than $600 and Sustainable Forest
Incentive Act payments.
You must be notified before Revenue Recapture is used. The claimant
agency must send you a written notice within five days after it notifies
the Department of Revenue. You have 45 days after receiving the notice
to request a hearing to contest a revenue recapture.
