If the tree is indeed dying, you should be able to get a special tree removal permit for a hazardous tree. Go to DDOT web page and fill out a form. An arborist will come out an inspect it.
Cost of removal will depend on size of tree and accessibility. Two companies we have used and who were reasonable are Ed's Tree Service and Walt's Tree Service. Definitely get multiple estimates because the prices can be all over the place for tree removal.