I don't think he knew who did it until after the part where she went out to fix the water and how she was acting.
There aren't all that many people that could have done it anyway, and I think the blood spot was a hand print that he could tell was a hell of a lot smaller than his own hand, which means a woman or a kid. Put together the idea of a woman doing it, and how Carol has been hard ass on keeping people alive, and it isn't a huge leap to try to see if she might have done it.
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