Children with Autism Spectrum Disorder (ASD) experience deficits in verbal and nonverbal communication skills including motor control, turn-taking, and emotion recognition. Innovative technology, such as socially assistive robots, has shown to be a viable method for Autism therapy. This paper presents a novel robot-based music-therapy platform for modeling and improving the social responses and behaviors of children with ASD. Our autonomous social interactive system consists of three modules. We adopted Short-time Fourier Transform and Levenshtein distance to fulfill the design requirements: a) "music detection" and b) "smart scoring and feedback", which allows NAO to understand music and provide additional practice and oral feedback to the users as applicable. We designed and implemented six Human-Robot-Interaction (HRI) sessions including four intervention sessions. Nine children with ASD and seven Typically Developing participated in a total of fifty HRI experimental sessions. Using our platform, we collected and analyzed data on social behavioral changes and emotion recognition using Electrodermal Activity (EDA) signals. The results of our experiments demonstrate most of the participants were able to complete motor control tasks with ~70% accuracy. Six out of the 9 ASD participants showed stable turn-taking behavior when playing music. The results of automated emotion classification using Support Vector Machines illustrate that emotional arousal in the ASD group can be detected and well recognized via EDA bio-signals. In summary, the results of our data analyses, including emotion classification using EDA signals, indicate that the proposed robot-music based therapy platform is an attractive and promising assistive tool to facilitate the improvement of fine motor control and turn-taking skills in children with ASD.