You almost certainly do not have to be concerned about this scenario but you might want to get confirmation from a tax professional familiar with Nebraska tax law.
Regardless, it does not appear as if the death of a joint tenant would result in inheritance tax being due and, further, the tax is typically imposed as part of the estate settlement process (i.e., prior to the assets of the estate being distributed).
See https://revenue.nebraska.gov/about/legal-information/regulations/chapter-17-inheritance-tax