This article from 1985 is an experimental article that compares normal children, children with autism and children with Down's syndrome on the theory of mind task. The task that was used was the false-belief task.
This task is a story which has Anne and Sally. Sally places a marble in place A. She leaves and Anne comes. Anne takes the marble from place A and puts it to place B. After that Anne leaves and Sally comes back. The question is where would Sally look for the marble. If they point to place A, then they have a 'theory of mind' or the ability to attribute the mental states to other people.
The results show that most of normal children and children with Dawn's syndrome (both around 85%) pass this task. But most children with autism do not (only 20% passed).
This article gives one of the possible explanation, when children with autism have problem with social skills.