The Omaha Municipal Code provides:
Sec. 20-195. - Possession or transportation of firearms.
(a) It shall be unlawful for any person to knowingly or purposely transport in any conveyance or in any other manner, or to possess off his own premises, any rifle, shotgun, air gun, air rifle, paint ball gun or machine gun unless the same is unloaded and contained in any enclosed gun case, or unloaded and broken down. The removal of the bolt from any such firearm or carrying the same in a holster type gun case without further breaking down such firearm shall not be deemed to be in compliance with the requirements of this section.
The section goes on to provide exclusions for law enforcement, National Guard, ROTC, etc.
BUT, being stopped with a loaded rifle or shotgun in your vehicle is a violation.
The penalty is a $500 fine, 6 months imprisonment or both.
I was not aware of this until recently. Different jurisdictions have different rules.