As humanoid social robots (HSRs) become more integrated into family environments, it is crucial to examine privacy concerns in child-robot interaction. This study examines how children and parents perceive privacy risks associated with HSRs, focusing on differences in their comfort levels across various usage scenarios. We conducted a user study with 38 parent-child dyads interacting with the HSR “NAO” using pre-programmed activities. Our findings revealed disparity in robot likability, smartness, and trustworthiness. These characteristics also influenced children’s willingness to share personal information (secrets). Parents and children showed significant differences in their comfort levels with sensor usage across different contextual scenarios, where parents expressed concerns about data collection, storage, and transfer, preferring supervised interactions, and emphasizing the need for transparency and control over robot interactions. These findings suggest that designing HSRs with clear privacy controls, child-friendly features, and parental oversight is essential to ensuring safer and more trusted interactions.