Data and materials that accompany the paper "Contestable Camera Cars: A Speculative Design Exploration of Public AI That Is Open and Responsive to Dispute". Applying a provisional framework for contestable AI, we use speculative design to create a concept video of a contestable camera car. Using this concept video, we then conduct semi-structured interviews with 17 civil servants who work with AI employed by a large northwestern European city. The resulting data is analyzed using reflexive thematic analysis to identify the main challenges facing the implementation of contestability in public AI.