This paper presents a series of results from a pilot study with ten participants to evaluate if children with autism spectrum disorder exhibit more social interaction interests when engaging with the parrot-inspired therapeutic robot, KiliRo, compared to with another human. Three sessions, each with different activities such as talking and singing that either the robot and a human encouraged the children to engage in, were conducted to monitor 12 types of social engagement behaviours in participants to compare the effects of engagement with a human and a parrot robot. The behaviours were recorded and analyzed using real-time video data of the interactions. The results indicate a positive influence of introducing the parrot robot to children on their social interaction. Also, the analyses revealed a significant difference in each of the session conducted based on the assessed 12 attributes, providing some indications for the potential benefits of human-robot interaction in therapeutic settings for children with autism spectrum disorder.