In Dallas, Texas, you generally do not need a permit to cut down a tree on your private property. However, there are some exceptions and regulations that you should be aware of. If the tree is located within the city's designated protected tree ordinance area or if it is a heritage tree, you may need to obtain a permit before removing it. Additionally, if the tree poses a danger or is causing damage to property, you may be required to provide documentation or evidence to support your decision to remove it. It is always recommended to check with the local authorities or consult with a professional arborist to ensure compliance with any regulations or restrictions before cutting down a tree in Dallas.