Welcome to the world of Kark gambits. He's testing reactions.
There are two possibilities. One is Star is DP and part of the act. The other is she isn't and Kark is also testing her reaction.
How are you supposed to act? I would assume surprised and very skeptical of Kark. Empty your mind from everything you know and try to piece together your thoughts as town. This is weird AF.
------------------------------ Kark Gambits Background: In Love Boat we had a D1 tracker claim. On D2 Kark counter claimed the tracker and we were about to lynch them. Just before day end Kark stirred up suspicion of someone else for NOT TURBOING (sound familiar?) and got a bunch of votes on them, but we ended up lynching the other trackers whom it turned out were scum, yay. The other one who didn't turbo got killed by mafia that night and flipped town.
Much later in this game we're almost in lylo and Kark has lead the lynch of a second scum when he flips his claim upside town and says he is on fact a cop who had investigated me and I was scum. I wasn't scum, I was an ordinary. He later retracted his cop claim. It was all a play to see how people would react and we lynched the person who immediately voted for me after Kark's claim (and had for long been suspicious of me) who was town.
Kark's cop claim made no sense when you thought about it because the first scum we caught thanks to the counter claim (whom he post cop claim claimed to have investigated N1) had claimed miller on D1...