I compleatly understand your concern, the reason I didn't specify any cultures is for the simple reason of how new I am. I do not know enough about any of the cultures to make any inferences as to what they would use, although I did see quite a few recurves in use by Elves in LOTR (here's a nice example)
I believe that's Legolas' bow...
but anyways, I believe the recurve was made originally in englad, although because it was so much harder and more expensive to make then a long bow (just look at the pictures) that it never really did see much action during medieval times.
if someone does want to connect a recurve to a certain race, or society, probably the best qualities would be that is can be made to look a lot more decorative then other types of bows, and it's a lot more "fluent" in draw and shot. it has a lot more curves, and it's a lot smoother then other types of bow. and it would be the mark of good craftsmanship.
and yeah, that was one of the best parts of the movie, is that you could tell an elven sword from a dwarven sword. and also the styles were very much like the races they came from. for example, the dwarves designs were very square, and streight. a lot of right angles, while the elves were curved and smooth.