The State of Wisconsin says, "If you are a nonresident or part year resident of Wisconsin and your Wisconsin gross income (including gambling winnings) is $2,000 or more, you must file a Wisconsin return using Form 1NPR. Gross income means all income (before deducting expenses) reportable to Wisconsin. You may obtain the Wisconsin Form 1NPR from the Wisconsin Department of Revenue website.
If your state of residence has an income tax, you may be able to claim a credit for tax paid to Wisconsin. Contact your state revenue department for the specific requirements in the state where you reside."
So the answer depends on how much you won. Please see www.revenue.wi.gov/DOR%20Publications/1104gambling.pdf for more information.