My brother-in-law found a similar greenish granite stone.  He took it to the University of Illinois to have it identified.  They told him Indians often buried such stones on the chest of a warrior or hunter-gatherer.  He was told the greenish cast came from the decaying body.  Such stones were tools to use in the next life.  I would guess the flat side was some kind of grinding stone, but that is only a guess.  Brother-in-law found a morter stone with a cup like depression.