Generally no because Nebraska uses the same itemized deductions as the federal government.
The federal government eliminated the itemized deduction for moving expenses as part of the changes to the tax laws.
However, there is an exception, and the deduction is allowed, if you moved into Nebraska and are filing a Part Year Resident Tax Return.
For more information and the source: http://www.revenue.nebraska.gov/tax/current/2011_indiv_bklt/line_66_adjust.html
[Edit: 3/30/2019 4:58 PST]
