Giving away a dog to someone else?

Hello. My cousin has a siberian husky that is about 1 year old now. The dog got into a fight with the neighbors dog that wondered into the backyard. He recently moved into a smaller house with a very little backyard, and wants to find his dog a better home with a bigger backyard because a 8x10 square is not okay for a husky whos used to being on an acre. If he gives the dog away and something happens...like the dog bites another dog or another person can you be liable for that???? if so, how can you make a contract to avoid that??? He fully intends on telling the people who takes the dog about previous incidences. Some1 please help. thanks