There is some evidence that pet therapy are effective for individuals with autism. The studies did not differentiate between children and adult though it is likely that the studies are focused on children.
This 2012 systematic review by O'Haire found increased social interaction and communication as well as a decrease in problem behaviors, autistic severity, and stress. There is a strong suspicion of publication bias and also a lack of control arms for comparison. O'Haire found 14 studies ranging from 1989 to 2012 that had outcome data for her review.
Another interesting 2012 French study by Grandgeorge et al) looked at the prosocial impact of having a pet in 260 families with children. What I thought was interesting was that having a pet since birth had minimal impact on the child which were the same rate as children without pets. However, if the family got a new pet after the age of 5, there was evidence of an increase in prosocial behavior.
Grandgeorge, M., Tordjman, S., Lazartigues, A., Lemonnier, E., Deleau, M., & Hausberger, M. (2012). Does Pet Arrival Trigger Prosocial Behaviors in Individuals with Autism? PLOS ONE, 7(8), e41739.
O’Haire, M. (2012). Animal-Assisted Intervention for Autism Spectrum Disorder: A Systematic Literature Review. Journal of Autism and Developmental Disorders. Vol 43, pg 1606–1622.