They have some body fat, but it's very little compared to some other bigger aquatic creatures. The percentage of body fat depends on the temperatures they live in, obviously.
http://www.leg.state.fl.us/statutes/index.cfm?App_mode=Display_Statute&Search_String=&URL=0300-0399/0379/Sections/0379.2431.html
(d) Except as may be authorized by the terms of a valid state permit issued pursuant to paragraph (c) or by the terms of a valid federal permit, it is unlawful for any person at any time, by any means, or in any manner intentionally or negligently to annoy, molest, harass, or disturb or attempt to molest, harass, or disturb any manatee; injure or harm or attempt to injure or harm any manatee; capture or collect or attempt to capture or collect any manatee; pursue, hunt, wound, or kill or attempt to pursue, hunt, wound, or kill any manatee; or possess, literally or constructively, any manatee or any part of any manatee.
I went on a trip in florida especially to find and observe manatees. You aren't allowed to be rough with them but if they come up to you then you are allowed to pet them
(d) Except as may be authorized by the terms of a valid state permit issued pursuant to paragraph (c) or by the terms of a valid federal permit, it is unlawful for any person at any time, by any means, or in any manner intentionally or negligently to annoy, molest, harass, or disturb or attempt to molest, harass, or disturb any manatee; injure or harm or attempt to injure or harm any manatee; capture or collect or attempt to capture or collect any manatee; pursue, hunt, wound, or kill or attempt to pursue, hunt, wound, or kill any manatee; or possess, literally or constructively, any manatee or any part of any manatee.