In most areas you would be allowed to cut the roots and any branches that hang over your property. However, you will not be allowed to put the branches on the neighbor's property.
One thing I would do is send her a certified letter advising her of this dangerous tree and asking her to take care of the problem. This would protect you if the tree did damage to your house or building she would be liable for the damage if you prove via the letter that she was aware of the danger from the tree.
One thing I would do is send her a certified letter advising her of this dangerous tree and asking her to take care of the problem. This would protect you if the tree did damage to your house or building she would be liable for the damage if you prove via the letter that she was aware of the danger from the tree.