The Iroquois had institutions that I might call democracy-ish. There is some question about whether the league itself was formed before or after contact with Europeans, but "before" seems probable, and so they were probably developed independently.

There were a number of republican states in ancient India, such as the Sakyas (The Buddha's tribe), Yaudheyas, and others, although how democracy-ish they were is difficult to say given the state of evidence (For the Licchavis, I think only male heads of households of the warrior caste could vote).