I've heard something similar to what NJ posted, trees with a trunk bigger than 4" need ARC approval, then I've heard it doesn't if they are Palms because they are classified as a grass. I've also heard there is a $500 fine if you remove without approval. I think I would check with ARC for be safe. Here are some older threads that may be helpful. You can also search anytime using the 'search' button at the top of the website.
Palm tree removal
Remove a palm tree and move a magnolia
Tree Removal
Tree removed - AB Landscaping]