My wife is Indian with US citizenship. As far as we've been able to tell, India does not allow dual citizenship (a quick google turns up many references to this, including Wikipedia). An Indian who becomes a US citizen can become an "Overseas Citizen of India" (OCI) which is not exactly the same as citizenship (you can't vote in India on that status, for example)
India does not allow dual citizenships. Rather people of Indian origin get the equivalent of a lifetime visa should they choose to be citizens of other countries, but this can be in no way equated with citizenship.