Melee weapons so far seem to have no effect on AI or players. I've swung a baseball bat, a shovel, and I've even stabbed with a screwdriver multiple times at zombies (and also at an unfriendly player). All attempts resulted in nothing happening. (Note that my fists work fine against zombies)
(EDITS) Melee weapons DO NOT WORK if they are RAISED (press space to lower and raise) If the weapon is lowered it works just fine (I've only tested this with an axe, however) They should work either way. Also, stabbing weapons such as the screwdriver do not cause damage. #Bugs
Bug being demonstrated with a hammer: http://www.youtube.com/watch?v=zlqy8lkO6tk&feature=youtu.be