Quick answer: life insurance not payable to the estate, the statutory homestead and family maintenance allowances, out-of-state property, and qualifying charitable gifts all escape this tax, on top of the class-based rates in Rates & Who Pays.
Life insurance is exempt, with one exception
The statutory family allowances aren't taxed
Money and property that immediate family members are entitled to under Nebraska's homestead allowance, exempt property right, and family maintenance allowance are exempt from inheritance tax. These are probate-law protections designed to support a surviving family during administration, and the legislature carved them out of the tax base entirely.
Out-of-state property is simply out of reach
Real estate and tangible personal property physically located outside Nebraska is fully exempt, regardless of where the decedent lived. Nebraska's inheritance tax reaches only property with a genuine connection to the state.
Qualifying charities are exempt
Transfers to charitable, religious, or educational organizations aren't taxed, provided the organization meets one of the qualifying conditions set out in Neb. Rev. Stat. §77-2007.04 — not every nonprofit automatically qualifies, so it's worth confirming a specific organization's status before assuming the exemption applies.
A local probate attorney can review your estate — many offer a free consultation.
An inherited interest valued at or below the applicable class exemption isn't taxed at all, and doesn't require a return simply because it exists — the exemption applies automatically to the lowest bracket of value received.