The use of partially autonomous robots in therapeutic contexts raises several ethical issues, starting with the degree of autonomy to be afforded to the robot. The more autonomous the robot, the less control therapists have over the robot-child interaction, raising the issue of where the responsibility for the robot’s actions lies. Autonomy also raises the problem of trust: are parents happy to have their child interact with a robot? Will the child trust the robot? The Eurobarometer study of public attitudes towards robots, shows that many people in Europe resist this idea of using robots in care. The aim of this paper is to investigate the ethical issues raised by the use of robots in therapy for children with ASD by means of a survey amongst caregivers, parents and teachers of children with ASD. We conclude that although in general stakeholders approve of using robots in therapy for children with ASD, it is wise to avoid replacing therapists by robots and to develop and use robots that have at what we call supervised autonomous interaction.