First, I don't believe the "law" (Title 23) covers rotten trees or who should pay for their removal whether they have fallen and blocked the road or not. This is a maintenance issue that should be brought up before the association members at your annual meeting.
Second, I feel that since the "emergency" has not yet occurred and if a majority of the members believe the situation is of consequence, the association officers should negotiate with the property owner involved and perhaps find a way to share in the expense of removing the trees. That way everyone wins to a degree. Good luck.