From http://lesswrong.com/lw/7o4/atheism_the_autism_spectrum/6x1c :

Developmentally, children's reasoning about God's mental states, and about other non-physical agents, tracks the cognitive development of mentalizing tendencies [19], [20].

• Lane JD, Wellman H, Evans EM (2010) Children's understanding of ordinary and extraordinary minds. Child Dev 81: 1475–1489.

  How and when do children develop an understanding of extraordinary mental capacities? The current study tested 56 preschoolers on false-belief and knowledge-ignorance tasks about the mental states of contrasting agents—some agents were ordinary humans, some had exceptional perceptual capacities, and others possessed extraordinary mental capacities. Results indicated that, in contrast to younger and older peers, children within a specific age range reliably attributed fallible, human-like capacities to ordinary humans and to several special agents (including God) for both tasks. These data lend critical support to an anthropomorphism hypothesis—which holds that children’s understanding of extraordinary minds is derived from their everyday intuitive psychology—and reconcile disparities between the findings of other studies on children’s understanding of extraordinary minds.

• Taylor M, Carlson SM (1997) The relation between individual differences in fantasy and theory of mind. Child Develop 68: 436–455.

  The relation between early fantasy/pretense and children's knowledge about mental life was examined in a study of 152 3- and 4-year-old boys and girls. Children were interviewed about their fantasy lives (e.g., imaginary companions, impersonation of imagined characters) and were given tasks assessing their level of pretend play and verbal intelligence. In a second session 1 week later, children were given a series of theory of mind tasks, including measures of appearance-reality, false belief, representational change, and perspective taking. The theory of mind tasks were significantly intercorrelated with the effects of verbal intelligence and age statistically controlled. Individual differences in fantasy/pretense were assessed by (1) identifying children who created imaginary characters, and (2) extracting factor scores from a combination of interview and behavioral measures. Each of these fantasy assessments was significantly related to the theory of mind performance of the 4-year-old children, independent of verbal intelligence.