Unfortunately no - MS is a state where that is a nonrefundable 3% tax withheld from all nonresidents' winnings.
However, you can file a nonresident MS state income tax return to report the MS winnings only and then claim a state tax credit in AL for the taxes that you paid on your MS nonresident state income tax return.
Just follow the TurboTax guide when working on your states (remembering to do your nonresident state return first) and TurboTax will do all the calculations and credits to your resident states return.
Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)
https://ttlc.intuit.com/replies/3300797
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