A CHP holder can carry inside the car on school property, but must secure the handgun in a locked container before exiting the vehicle.
As far as a cased rifle or shotgun locked in the trunk, I am thinking that is legal if the holder is not a prohibited person. A school employee could be fired for violating school policy.
I am sure about a student though, that there was a change in the law concerning this last year, making it a felony to have a gun on the campus of a school, and I was concerned about the high school trap teams getting caught up in it.
I seem to recall a case in Omaha of a (adult) guy with long guns in the back of his truck on school grounds, and having a scuffle with some gang bangers. But that was before the law was changed
28-1204.04 Unlawful Possession of A Firearm at a School; Penalty; Exceptions; Confiscation of Certain Firearms; Disposition.
(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.
(e) firearms contained within a private vehicle operated by a nonstudent adult which are not loaded and
(i)are encased or
(ii) are in a locked firearm rack that is on a motor vehicle, or
(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.