I agree with Matt -- make sure to check your laws.
In most places that I'm aware of in the states, it's usually illegal to collect a kill by a car. The laws were put in place to prevent people taking deer out of season, or taking more deer than their tags would allow, etc. by claiming a car hit and mercy killing.
You can kill the deer if it's injured, you just can't harvest anything from it. My guess is New Hampshire law is the same as the other dozen or so states I'm aware of. But if you've got a valid tag, then you can give that up to harvest although fatal car hits usually spoil a lot of meat.