No. The city's property maintenance code has rules about low-hanging branches, but it stops short of requiring property owners to remove trees.
Specifically, if a tree limb hangs lower than 13.5 feet above the street, 7 feet above the sidewalk, or 12 feet above an alley, the city generally requires the owner to remove the tree limb, whether healthy or not.
Dead trees pose a significant liability to risk to property owners, however. Standing dead trees are dangerous and unpredictable. Those near other homes and buildings, or roads and pathways can cause serious damage and even death when they fall.
The general rule of thumb: if the tree is on your land, you're liable for any loss or damage caused when it, or any part of it, falls.
The Texas Forest Service has more information on how to handle hazardous trees here.
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FEATURED PHOTO: A car was crushed by a falling tree on Maple Avenue in Dallas recently. File photo/The Dallas Morning News