Delaware dog liability for owners of strong dogs
Delaware is one of the states that covers all injuries a dog causes, not only bites.

The owner liability statute
The dogbitelaw.com summary of Delaware dog bite law quotes Delaware's statute: the owner of a dog is liable in damages for any injury, death or loss to a person or property caused by the dog, unless the victim was committing or attempting a trespass or other criminal offense, or was teasing, tormenting or abusing the dog. The site notes the statute reaches non-bite injuries and losses to property.
Other routes for a victim
The same source says Delaware also allows claims in negligence, negligence per se and scienter, and says the rule against dogs running at large without the owner's control is treated as negligence per se when violated.
The dangerous dog code
The Delaware Code Title 16, Chapter 30F, Subchapter V lets the Justice of the Peace Court declare a dog dangerous. An owner of a dog declared dangerous must, among other duties, carry at least $100,000 in liability insurance, keep the dog in a proper enclosure or muzzled on a non-retractable leash of 6 feet or less, post a warning sign, and have the dog microchipped. The same subchapter says a dog defending a person within the immediate vicinity from an attack is not to be considered dangerous or potentially dangerous.
Insurance and housing
Tell your insurer what dog is coming and read your lease or community rules first. State law does not override either.
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