Therapeutic pet robots designed to help humans with various medical conditions could play a vital role in physiological, psychological and social-interaction interventions for children with autism spectrum disorder (ASD). In this paper, we report our findings from a robot-assisted therapeutic study conducted over seven weeks to investigate the changes in stress levels of children with ASD. For this study, we used the parrot-inspired therapeutic robot, KiliRo, we developed and investigated urinary and salivary samples of participating children to report changes in stress levels before and after interacting with the robot. This is a pioneering human-robot interaction study to investigate the effects of robot-assisted therapy using salivary samples. The results show that the bio-inspired robot-assisted therapy can significantly help reduce the stress levels of children with ASD.