I'm going to assume that by God you mean my particular version of God, which is my case is Judeo-Christian. I am a theist and I WOULD release the information to the public, for one main reason.
If I had the proof and didn't spread it, I would be (at least in my own view) personally responsible for the deliberate deception of every single person who followed my God. All the hopes of Heaven, all the prayers, all the disappointments, all the time that would be wasted thinking of the afterlife that won't come and not enjoying the one we do have, and lots more would all be squarely on my shoulders. Every violent disagreement over some aspect of the non-existant deity would leave blood on my hands. EVERYTHING. I would not wish to be personally responsible for all of that. And not just things that obvious. Every person who died because money went to megachurches and not cancer research, every person who died because of religious opposition to science slowed a cure down, every possible economic problem that might be fixed if money was taken away from the (I would at that point know to be) useless cause of religion to my God would also be squarely on my shoulders for not preventing it. Every negative possible thing that could be attributed to any religions pertaining to my God that transpired from my not revealing this evidence would be entirely my fault. In the words of the lolcats, DO NOT WANT.
And plus, if I'm merely certain, but could still be wrong about it showing God to not exist, then I would want to find out if it were right or wrong, which would mean spreading it to people who could tell me if it were correct or not.
Metherion