Monokuma gave out doll that looked like the person. Now you had two options, either give it to another person for trust or keep it, But the other CANT know. And since you trusted Kokichi enough you gave him the doll without thinking twice. And of course Oma accepted it.

Now when you gave him the doll you could feel everything he touched on your body. Which was weird for you, why could you feel it? And when Kokichi pulled the dolls hair your hair got pulled so you let out a yelp. This made Oma's lips turn into a twisted smile, he let out a laugh. "Ah! seems like this isn't any normal kind of doll. It's a voodoo! I would say 'aw thats so bad!' But i would be lying." With that he started to play around with the doll, he didnt care if he touched you in the wrong place, this was exciting and a surely a funny sight to look at.