If you are a military spouse living in Nebraska only because your service member is stationed here, the income you earn is exempt from Nebraska income tax.
There is nothing to file with the state to qualify. Ask your employer to stop withholding Nebraska income tax on the basis of the military spouse residency rules, using the withholding paperwork described on the Department of Revenue's military spouse FAQ page, and file a Nebraska return to claim a refund of any Nebraska tax already withheld.
Your marriage certificate, your service member's orders assigning them to Nebraska, and proof that you and your service member are legal residents of the same other state, such as a driver license or voter registration.