What should I do about a neighbor's tree that is leaning towards my house?

Since 2002, I have owned a house and the neighbor's dead pine tree has been leaning towards it. On several occasions I have had trees removed from my yard and suggested that the neighbor hire the same people to remove the dead tree in her yard. But she has not. I no longer live in the house, but my tenant informs me that the tree is now leaning even more dangerously towards the house. I am now sending the neighbor a certified letter requesting that the tree be removed. I am sending a copy to my insurance company. Is there anything else I should do? Can I find out who her insurance company is and send them a copy of the letter as well? How would I find this out? Or would I request that my insurance company contacts her insurance company? I don't know how this all works. One last question -- what happens if they do not sign for the certified letter? Are they still liable if the tree falls on my house? Thanks