Most perfumes are alcohol based, and alcohol evaporates much more quickly than water - hence the cooling effect you feel on your skin when you dab on perfume.
If you mean complete evapouration I would have to dissagree with the above. Wilst they are correct to a point, the fragrance in the perfume is likely to be made up from oils which evapourate slower than water (hence the smell hangs around for a bit). Initially the perfume will evapourate faster as alcohol is lost, then the purfume oils will remain, evapourating slowly over a few hours,.