It depends on the state where you received your gambling winnings. If you do not meet the filing threshold for a nonresident to file in the nonresident state, then you will not have any filing requirements related to the nonresident state. The fact that no withholdings were taken out of your winnings does not exempt you from filing in that nonresident state.
Please note that in any case, you will need to include the winnings on both your federal and state income tax returns (if your resident state has a state income tax filing requirement).
Here is a link to the State
Department of Revenue Contacts websites, just review the "nonresident filing requirements" section and gambling winnings by nonresidents.