You might wish to check out
Nebraska Statue 28-1204.04, which states in part:
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(1) Any person who possesses a firearm in a school, on school grounds, in a school-owned vehicle, or at a school-sponsored activity or athletic event is guilty of the offense of unlawful possession of a firearm at a school. Unlawful possession of a firearm at a school is a Class IV felony.
This subsection
shall not apply to:
(a-e) [Usual exemptions, such as police, ROTC, training, etc., etc.]
(f) a handgun carried as a concealed handgun by a valid holder of a permit issued under the Concealed Handgun Permit Act in a vehicle or on his or her person while riding in or on a vehicle into or onto any parking area, which is open to the public and used by a school if, prior to exiting the vehicle, the handgun is locked inside the glove box, trunk, or other compartment of the vehicle, a storage box securely attached to the vehicle, or,
if the vehicle is a motorcycle, a hardened compartment securely attached to the motorcycle while the vehicle is in or on such parking area, except as prohibited by federal law.
For purposes of this subsection, encased means enclosed in a case that is expressly made for the purpose of containing a firearm and that is completely zipped, snapped, buckled, tied, or otherwise fastened with no part of the firearm exposed.
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It's always a good idea to go to the actual posted NE statutes at
http://www.legislature.ne.gov/laws/browse-statutes.php for the latest, updated official wording.
May you never draw your handgun in fear nor anger.