I couldn't tell you whether it's a fake or not but I suggest you take a look at this page about facsimile confederate notes: http://www.rebelstatescurrency.com/reproductions.html
If I am not mistaken the CSA's early notes were not printed on the back. Your's is printed on the back. In fact, the back design is exactly the same as the front except it is green. It looks like even the signatures are green (which would make no sense whatsoever.) Your photos are not the best but the signatures appear to have been printed with the note. The signatures on a genuine note would have been signed separately and using a different ink. Based on the above observations I feel safe in saying your note is not genuine.