Cognitive dysfunction including disrupted behavioral flexibility is central to neurodevelopmental disorders such as Autism Spectrum Disorder (ASD). A cognitive measure that assesses relational memory, and the ability to flexibly assimilate and transfer learned information is transitive inference. Transitive inference is highly conserved across vertebrates and disrupted in cognitive disorders. Here, we examined how mutations in the synaptic cell-adhesion molecule neuroligin-3 (Nlgn3) that have been documented in ASD impact relational memory and behavioral flexibility. We first refined a rodent touchscreen assay to measure visual transitive inference, then assessed two mouse models of Nlgn3 dysfunction (Nlgn3−/y and Nlgn3R451C). Deep analysis of touchscreen behavioral data at a trial level established we could measure trajectories in flexible responding and changes in processing speed as cognitive load increased. We show that gene mutations in Nlgn3 do not disrupt relational memory, but significantly impact flexible responding. Our study presents the first analysis of reaction times in a rodent transitive inference test, highlighting response latencies from the touchscreen system are useful indicators of processing demands or decision-making processes. These findings expand our understanding of how dysfunction of key components of synaptic signaling complexes impact distinct cognitive processes disrupted in neurodevelopmental disorders, and advance our approaches for dissecting rodent behavioral assays to provide greater insights into clinically relevant cognitive symptoms.