You do not owe Louisiana income tax on wages you earn in Louisiana if you are a nonresident military spouse living in the state only because of your husband or wife’s orders. You may still have to file an income tax return in your own state of residence.
There is nothing to file with Louisiana to claim the exemption itself. Give your employer your residency information so Louisiana tax is not withheld, and contact the Louisiana Department of Revenue if tax was already withheld so you can claim a refund.
Your service member spouse’s orders assigning them to Louisiana, your marriage certificate, and proof of your residency in another state such as a driver license or voter registration.