I haven't seen the video, but based on what I've read, I don't think Sharpton's saying that Romney, specifically, does not believe in God. If anything, he's saying that ALL Republicans don't believe in God, which is more accurate anyway. Well, they believe in God, but 'God' is just a tool they use to rationalize murder, rape, and theft.
Further, the Mormons don't like to talk about God or even the bible, for that matter. They consider the bible to be 'flawed', whereas the Book of Mormon is 'perfect'. Their god figure is known as 'Heavenly Father' or 'Father in Heaven' and if you don't call him by that name, people will look at you funny.