Hypothetically speaking, if there was an entry that was so far and away better than the others that we judges could not in good conscience choose another, and it also won the community vote, then that entry could win both. There's nothing in the rules that say the winners must be different entries.
I doubt it'll ever happen though. There hasn't yet been a month where we didn't have at least a couple entries make it into our winner contention talk, and more often it's 3+ due to each of us contest managers having a different personal favorite. :P