D.D.
You haven't said what the "adult behaviour" is so I'm guessing. How old is your daughter?
Girls tend to be more sexually aware than boys even at a young age. However, they usually don't engage in adult behaviour unless they have experienced it or seen it on TV or somewhere else. Has she been exposed to inappropriate things on TV or the computer?
Maybe she is being sexually abused or approached by someone. I would talk to the teachers about it immediately and change her circumstances. Maybe another child is causing this? Maybe someone in your circle of friends/family? Is your daughter trying to tell you something you missed? It happened to me.
My daughters sometimes engage in inappropriate behaviour - but it's definitely child not adult-like. I tell them it's inappropriate, and also, in the very young you want to "extinguish" the behaviour by not talking about it and not reacting to it, at least until you have had some time to think it over.
I wouldn't punish her, but I would be the detective to find out what happened, then teach her appropriate behaviour to replace the inappropriate behaviour.