Title 483-B9 section V B 2 C
http://www.gencourt.state.nh.us/rsa/...-B/483-B-9.htm
(C) Dead, diseased, or unsafe, trees, limbs, saplings, or shrubs that pose a hazard to structures or have the potential to cause personal injury may be removed regardless of any requirements that pertain to the natural woodland buffer under this chapter. Such exemptions shall not be used to contravene the intent of the law.
If the tree is falling or unsafe, it can be removed without a permit. The owner should take pictures first, just in case there are questions afterwards. The picture in this thread, compared with a current picture, should be enough. The stump must be left in the ground to control erosion.