According to both Judge Judy and Judge Milian (on Peoples Court)
If it is a healthy tree and hit by lightening or blown over and falls on your property it's your problem however if you had previously
notified your neighbor it was a dying or dead or sick tree and then it fell he/she would be responsible. Can't blame God or his/her weather makers. Bottom line is if it is a "sick/dying" tree notify your neighbor in writing, email or text to CYA. You CAN cut a tree anywhere it hangs over your property line without permission from the owner.