Lawyer Andrew Branca recommends having a less-than-deadly alternative to defend against attacks that aren't serious enough to justify defense with deadly force. He cites FBI data that less-than-deadly attacks are many times more common than deadly ones. Pepper spray is one of the suggested alternatives.
As near as I can tell, pepper spray is completely legal to carry. Nebraska has no laws that regulate it. It doesn't meet the legal definition of a weapon.
What is the legal status of pepper spray in places where concealed handguns are illegal even if they aren't posted (courthouses, police stations, hospitals, schools, etc.)? How about places that post signs reading, "No guns or other weapons" (e.g. Omaha Public Library)? Unless you have to empty your pockets at an entrance checkpoint or attract attention by causing a disturbance, pepper spray is unlikely to be found. My uneducated guess is that such places are equivalent to jurisdictions where "No Guns" signs do not have the force of law. It's not illegal to carry into them but, if found out, you can be ordered to leave on pain of conviction for trespassing if you refuse.
