Normally, "file exempt" means "exempt from withholding" which is possible in certain circumstances. Please read this TurboTax blog entry ''Can I File Exempt & Still Get a Tax Refund?"
Also note that you generally pay taxes in the state where you live AND in the state(s) where you work. So, as xmasbaby0 says, you would file a non-resident return for Iowa and a resident return for Nebraska.
The issue of double taxation is usually solved by one state giving you a credit for all taxes paid to another state on the same income.
Filing exempt does not excuse you from filing at all.
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