That has been asked before, here's a couple of responses.
Palm Tree Removal
Palm Tree Removal
Even though they're dead, you will probably be best to get ARC (Architectural Review Committee) Approval. They'll probably ask for a letter from an arborist. I don't know any, but once I needed advice on a palm tree and I contacted Jim Davis, Director of Sumter County Agriculture extension University of Florida. I emailed him photos and he sent a reply in a couple of days. Here's his contact info.
Sumter County - Central
Specialty: Agriculture/Community Development
7620 SR 471 Ste 2
Bushnell, FL 33513-8716
dvisshdn@ufl.edu
Tel: (352) 569-6866 Fax: (352) 569-6861