In the end, if you're a civilian and Picard gives you an order, I imagine you're expected to follow it unless you have some grounds for claiming it's illegal or otherwise inappropriate (he's unlikely to order a civilian to take command of the saucer section, for instance).
Having seen no real evidence of self-government, I really doubt the civilians had such a thing. Sure, Picard probably didn't decide things like classes...that's what his subordinates and possibly a civilian liaison are for, much as how for most of the crew Picard didn't directly handle evaluations. He's captain of the ship, not a micromanager, but that doesn't change the fact that as the ultimate authority on board everyone is technically in his chain of command, at least in terms of there being a power dynamic between them.
Aside: I just finished watching NuBSG myself. Interesting series, and sometimes a gripping one. My understanding is that there's a fair amount of disappointment with how it ends, but I'm not sure what the nature of the complaints are, nor that I would share them. But even in BSG, where there was a civilian government, the commander of Galactica was ultimately responsible for military matters and with regards to at least the civilians on Galactica could be construed as having authority over them. Similarly, I imagine the captains of other ships in the fleet had authority over the civilians on their ships, while the commander of Galactica had ultimately authority over military matters...and yes, there was sometimes tension over what constituted a military matter.