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Autism spectral disorder (ASD) is a highly prevalent neurodevelopmental disorder characterized by deficits in communication and social interaction. Head-nodding, a kind of visual backchannels, is used to co-construct the conversation and is crucial to smooth social interaction. In the present study, we quantitively analyze how head-nodding relates to speech turn-taking and prosodic change in Japanese conversation. The results showed that nodding was less frequently observed in ASD participants, especially around speakers' turn transitions, whereas it was notable just before and after turn-taking in individuals with typical development (TD). Analysis using 16 sec of long-time sliding segments revealed that synchronization between nod frequency and mean vocal intensity was higher in the TD group than in the ASD group. Classification by a support vector machine (SVM) using these proposed features achieved high performance with an accuracy of 91.1% and an F-measure of 0.942. In addition, the results indicated an optimal way of nodding according to turn-ending and emphasis, which could provide standard responses for reference or feedback in social skill training for people with ASD. Furthermore, the natural timing of nodding implied by the results can also be applied to developing interactive responses in humanoid robots or computer graphic (CG) agents.