Since the diagnosis of autism spectrum disorder (ASD) relies heavily on behavioral observations by experienced clinician, we seek to investigate whether parts of this job can be autonomously performed by a humanoid robot using only sensors available on-board. To that end, we developed a robot-assisted ASD diagnostic protocol. In this work we propose the Partially observable Markov decision process (POMDP) framework for such protocol which enables the robot to infer information about the state of the child based on observations of child's behavior. We extend our previous work by developing a protocol POMDP model which uses tasks of the protocol as actions. We devise a method to interface protocol and task models by using belief at the end of a task to generate observations for the protocol POMDP, resulting in a hierarchical POMDP framework. We evaluate our approach through an exploratory study with fifteen children (seven typically developing and eight with ASD).