More:
The girl, Milly, says of the boy, Eric, "They think he's autistic." He's never spoken a word in his life. He doesn't like to be around people. And an institution wants to take him but Mrs Sherman (his teacher?) thinks he's better among people.
Eric has the belief that he knew the plane his parents were on was going to crash and the only way he could save them was by being an airplane. And he's been one ever since and is in the habit of walking around on the roof.
One night Milly sees him being brought home in a straightjacket. She lives with an uncle (an alcoholic?) after her father died from cancer.

There is a low key romance in which Milly does all the running.

Initially Milly's teacher asks her to help Eric as a project. Her response is "He won't do anything on his own. " but he does start to mimic her. She finds it all tedious. However when she falls 50 feet from a bridge without hurting herself she claims she was rescued by Eric. She does have concussion and sees a psychiatrist from whom she learns that her father committed suicide. Her father did have cancer but if the death certificate had stated suicide they wouldn't have got insurance money.
When Milly comes out of hospital Eric has been taken away to an institute. She's not allowed to visit him, only relatives may. Eric escapes and comes back home. Things get really silly (these scenes including the fall from the bridge are not indicated as fantasy) when she and Eric fly around like Peter and Wendy. Then he speaks to tell her he loves her but flies away and is never seen again. Meanwhile scientists do tests on her.