The homeowner is liable for the damages and responsible for the tree removal. 
These trees are managed by the City of Bellevue, and if they pose a threat to a homeowners property due to disease, rot, weak root system, etc. it is the responsibility of the home owner to notify the City to have the tree(s) in question removed. Some of these trees are quite tall and their ability to reach out and hit your house are surprisingly high. To report a potentially unhealth tree, call 425-452-6855 or email parksweb@bellevuewa.gov