Lieberman claims he will be a Democrat until at least the late hours of August 8, 2006.
From what I understand about CT election law, what this likely means is that Lieberman is going to start collecting the 7500 signatures he needs to get on the ballot as an independent before the August primary, as he'll have to file them the very next day. So, if you're a CT resident be on the lookout for people with clipboards asking for your signature to get Lieberman on the ballot. I imagine he'll want to have this be below the radar for as long as possible so it'll be somewhat of a stealth campaign.
...ah, I've been informed that Joe won't really be able to do a stealth campaign. It'll be a part of the public record as soon as he even starts the process. So, the day Joe starts to jump we'll know.