Yes you can sue your neighbor if the tree is on his property and the tree falls on your house and damages your house.
The neighbor needs to keep the tree branches cleared of your house so that they do not cause damage but you can sometimes work with them and just have the tree branches cut away from your house.
If your neighbor refuses to cut tree branches away from your house you can also sue the neighbor to pay for the cutting of the tree branches even if no damage was done.
Also your homeowners insurance should cover damage to your home if a neighbors tree falls on it or even the neighbors homeowners insurance should pay for it as well.
If your neighbors tree falls on your house and damages it then you should speak with the neighbor first about getting their insurance to pay for it.
Also make a claim with your own homeowners insurance as they will usually pay for the damages to your home.
If not then take the neighbor to court and sue them to make them pay for the damage.