Insurance Problem – HELP!!

Next door has a massive eucalyptus tree right next to my house, with branches leaning over the fence & my house.

The tree is about 50 ft tall and would fall right across my house cutting it in two. A mess.

I have insurance on the building, but I want to limit my liability if the tree damages the house.

I understand if I ask or help the neighbour to cut the tree down and any part falls on the house damaging it, then I am liable because I assisted or instigated the action.

Is there any other way that legally I can do anything now to negate my liability and put it all back on the neighbour. Such as writing them a letter to say I accept no responsibility/liability if the tree falls on my house.

I don’t want hassles with my insurance company in the event of an accident. The tree is extremely old and dry and does not look solid & in good condition hence my concerns.

Hope you can assist

with thanks

Juls [anxious]