While it is possible, the penny hits a terminal velocity and it is not really that dangerous. In most cases it would hurt a great deal, could cut the skin or leave a large welt, but it is not going to be fatal.
Urban myths to the contrary, no. Objects falling through AIR reach a maximum speed that is limited by air resistance, A penny will tumble, and reach a max speed that, when combined with it's weight,...
I say NO. If you mean it is dropped and falls vertically.
Discover Channel's "Myth Busters" tried to determine if a bullet would kill you if it was fired directly vertical and falls on its own....