I feel like if you carried the cat in to just order or if it was in one of those cat-back packs it would probably be fine. I'm not quite sure about hanging out inside with a cat while you drink tea. I would probably call and ask if that was the case.
I suspect Madison board of health law would prohibit animals inside a restaurant unless it's a service animal.
Unsure. I don't think I've ever seen one inside personally, you might have to call to get a definitive answer. FWIW I did bring my dog once, but he stayed in the outside seating area the entire time
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