Planetarian - General Discussion

Let’s get some life in here…

As the story of Planetarian progressed, the protagonist started to treat the robot girl Yumemi more like an actual person, a human.
She behaved like a human, expressed joy, worry and other human emotions. Maybe some of you remember a small flashback of the main character where he mentioned his late colleague who had visited the planetarium before him. And he had warned him to not talk to that robot in there. Possibly because she’s just so human-like, or there was just something about her personality, that he couldn’t get her out of his head or something.

Therefore, let’s discuss the following question:
At what point can someone be considered ‘human’, or say, ‘a person’? Do circumstances exist where a far enough advanced robot, AI, doll or something along those lines, can become a ‘person’ ?