‘I am a guest of my girlfriend who owns a town home. A large tree branch that has dead portions to it fell and did significant damage to my truck. Is the association responsible for the damages? Do I need to prove negligence of improper care of the dead portions of the tree?’

Whose tree is it? If the tree belongs to the HOA, then most likely accidental damage caused by the tree would be covered by the HOA’s insurance. However, if the town home includes any private yard area and
the tree is inside that area, it might be your girlfriend’s tree.

The details of what is required for a claim in this type of case do vary from state to state. However, I would suggest you first approach the HOA by letting them know what happened, and asking if this is something their insurance will cover. If they refuse to submit the claim or it is rejected, then you can check with a local attorney to determine whether there is a clear enough case under your state’s law to make it worth pursuing further.