Cognitive abilities are impaired in neurodevelopmental disorders, including autism spectrum disorder (ASD) and schizophrenia. Preclinical models with strong endophenotypes relevant to cognitive dysfunctions offer a valuable resource for therapeutic development. However, improved assays to test higher order cognition are needed. We employed touchscreen technology to design a complex transitive inference (TI) assay that requires cognitive flexibility and relational learning. C57BL/6J (B6) mice with good cognitive skills and BTBR T+tf/J (BTBR), a model of ASD with cognitive deficits, were evaluated in simple and complex touchscreen assays. Both B6 and BTBR acquired visual discrimination and reversal. BTBR displayed deficits on components of TI, when 4 stimuli pairs were interspersed, which required flexible integrated knowledge. BTBR displayed impairment on the A > E inference, analogous to the A > E deficit in ASD. B6 and BTBR mice both reached criterion on the B > D comparison, unlike the B > D impairment in schizophrenia. These results demonstrate that mice are capable of complex discriminations and higher order tasks using methods and equipment paralleling those used in humans. Our discovery that a mouse model of ASD displays a TI deficit similar to humans with ASD supports the use of the touchscreen technology for complex cognitive tasks in mouse models of neurodevelopmental disorders.