Complex sentence: The structure of all New England town governments is based on the same "three legged stool" as the Federal government which has the executive (president), legislative (congress) and judicial (supreme court) branches.
Split into simpler sentences: The structure of all New England town governments is based on the same three legged stool as the Federal government. At the Fed level we have the executive (president), legislative (congress) and judicial (supreme court) branches.