I am a bit scpetical about this. To my knowledge, there is nothing indicating neanderthals ever lived in the new world. Their range was europe and the midle east. Also, they hunted BIG game, with traps and spears, not bows. If, however, "neanderthals" is (falsely) used as a synonyme for "prehistoric humans", the use of recurve bows is plausible, yet there remains some dispute since when exactly real composite bows were made. Some say since the mesolititic, judging fom pictures of bows that look like compounds from their dimensions (i.e. they were shorter than would be expected from a purely wooden bow). However, some cultures use short bows with a much shorter draw than we do, and poison them to compensate for the lack of projectile energy.
