neighbour wants me to keep my tree

Hi Guys,
looking for some advise.
I have a 30 years old tree in my backyard going 45' into my neighbor's yard.
I wanted to cut the tree but my neighbor insists to have the tree there and she accepted verbally to accept all the future issues three can cause for fence or ....
My question is, if for any reason the tree falls down into her house and damage her garden, am I responsible for the damage?
should I get her to right and sign on a paper that she accepts all these responsibilities and will this be sufficient in court?
and is there a formal form to transfer these responsibilities to neighbor ?
Thanks

I guess it might depend where you are, but here in NSW I had my mature gum tree, which was perfectly healthy, fall down in a storm.

All the water finally affected the base and it fell on a neighboring townhouse.

It turns out that if its healthy and there are no obvious signs it should be taken care of, its an act of god, and no one is responsible, and if it falls on your stuff, you need to be insured. If it falls on someone else's they need to be insured.

That said, in your case, I would ask the neighbour to write or sign a letter saying that they like the tree and that they would like it to remain and that they would notify you as soon as they think it is a risk to them.

Generally coverd by insurance, but if there is a known problem with the tree (eg. a bad arborist report), the insurance company won't pay up.

may be crazy but when she signs waver get a copy to your council.Have it signed for so you know they received it.