Strict liability for any injury, not just bites
Neb. Rev. Stat. 54-601 declares dogs personal property and makes the owner liable for any and all damages to any person, other than a trespasser, who is bitten, and to any person injured, worried or chased by the dog. The Nebraska Supreme Court has described it as a cause of action based on strict liability.
Nebraska has no one-bite rule, and the statute reaches knockdowns and scratches. The recognized limits are trespass, intentional provocation, and a possible playful-conduct exception.