Nature has a recent "Podcast Extra," an extended interview with physicist Paul Davies that I listened to while injuring my foot on a trail run. He's got an interesting book, The Eerie Silence, about the failure so far of SETI to detect alien intelligence and what the next steps might be.
Davies talked about his position as chair of the SETI post-detection task group, which is where the not-very-secret conspiracy issue arises and where he said some things that contradicted statements I've heard from SETI guy, Seth Shostak. He said that if they receive a signal demonstrating alien intelligence that has no policy implications beyond the demonstration of its existence, then the world should be told. If, however, the communication has implications like instructions for how to transform our technology, the potential disruptive impact means we shouldn't immediately disclose the news. He also said we should be very careful and controlling of what information humanity should send in response.
I'm just going off of memory, but I think Shostak has said the exact opposite - that all information should be disclosed, and that a cacophony of signals sent to the aliens might actually give them a better idea about us than careful control would. I think Shostak's right.
As a practical matter, I don't think SETI scientists are capable of keeping secret something this important, and I'm not sure they and anyone they recruit in the decision-making has the right to keep the information secret. And as I'm certain I heard Shostak say, it's not possible from stopping anyone with a two-bit radio antennae from making their own broadcasts in response.
Otherwise, Davies had some interesting stuff to say, and his book might be worth picking up.