It depends -
If the winnings are greater than $1,000 and you have to file a US federal income tax return (because you meet the income threshold to file), then you will need to file an IA nonresident state income tax return to report your IA -sourced gambling winnings. Otherwise you will just report the winnings on both your federal and NE resident state income tax return.
If you are required to file a nonresident IA return to report these winnings, you will be able to claim a state income tax credit on your NE resident state income tax return for any taxes paid in IA on income that is being taxed in both state.
Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)