"Religious Belief Systems of Persons with High Functioning Autism":

ABSTRACT: This paper investigates the proposal that individual differences in belief will reflect cognitive processing styles, with high functioning autism being an extreme style that will predispose towards nonbelief (atheism and agnosticism). This view was supported by content analysis of discussion forums about religion on an autism website (covering 192 unique posters), and by a survey that included 61 persons with HFA. Persons with autistic spectrum disorder were much more likely than those in our neurotypical comparison group to identify as atheist or agnostic, and, if religious, were more likely to construct their own religious belief system. Nonbelief was also higher in those who were attracted to systemizing activities, as measured by the Systemizing Quotient.

...Personality psychologists have identified two styles of reasoning: emphasis on logic and emphasis on intuition (Demaria, Kassinove & Dill 1989). As the Autism Spectrum Disorder (ASD) thinking traits are indicative of a logical cognitive style, we developed a set of thinking traits that would be represented in postings by neurotypical (NT) individuals.
The NT thinking traits embody the complimentary attributes of the ASD thinking traits. For example the NT thinking trait "emphasis on intuition" was developed to compliment the ASD thinking trait "emphasis on logic". The NT thinking traits looked for in the postings were emphasis on intuition, oriented towards social rewards, empathizing, symbolic fluidity/gestalt thinking, and openness to experience.
...[discussion forum analysis:] Religious beliefs were found to differ significantly between the HFA and NT populations, χ2 (12, N=387)= 43.69, p < .01. As shown in Figure 1, individuals with HFA were less likely to belong to an organized religion than their NT counterparts and were more likely to create their own religious belief system. The "own-construction" category comprised 16% of the HFA population as compared to only 6% of the NT population. HFA individuals also demonstrated higher rates of non-belief identities such as Atheism (26%) and Agnosticism (17%). In the NT group, only 17% of the population were Atheists and 10% were Agnostic.
...[survey:] Religious beliefs were found to differ significantly between the HFA and NT populations, __ (12, N= 166) = 22.698, p < .01. As was found in the content analysis of discussion forums, HFA questionnaire respondents were less likely than their NT counterparts to belong to an organized religion. HFA individuals were more likely to be atheist than were NT individuals. The "own construction" belief category was also found to be proportionally greater in the HFA population than in the NT population (see Figure 3).
...[from conclusion]: We suggest that individual differences in cognitive styles is an important predictor of human belief systems, including religious belief. An extreme type of cognitive style is high functioning autism. The 2 studies reported here found that individuals with HFA have a higher rate than neurotypicals of endorsing atheism and agnosticism. HFA individuals thus resemble another group of high-systemizers (scientists), who also reject religious belief at a relatively high rate.

Caldwell-Harris et al 2011.

Mostly as one would expect, although I am troubled that the second survey did not find any difference in agnostics, only the other categories.

See also: "How to be deader than dead".