Per RSA 466:28, killing dogs is legal in cases of self-defense and the protection of domestic animals:

"Any person may kill a dog that suddenly assaults the person while such person is peaceably walking or riding without the enclosure of its owner or keeper; and any person may kill a dog that is found out of the enclosure or immediate care of its owner or keeper worrying, wounding, or killing sheep, lambs, fowl, or other domestic animals."

http://www.gencourt.state.nh.us/rsa/html/XLV/466/466-mrg.htm