我在網上查是owner of the tree 不用管鄰居的fence damage, 和檸檬說的處理shed 是一回事

Whoever owns the damaged property is responsible to get the damage repaired – not the owner of the tree. 

“In mst American states, if your tree or any part of it falls on your neighbors' property and causes damage through no fault of your own (due perhaps to a snow storm, winds, hurricane, or other so-called "act of God"), you are not responsible. Your neighbors will have to file a claim with their own property insurer if they want to be reimbursed for their loss."