Local governments increasingly use artificial intelligence (AI) for automated decision-making. Contestability, making systems responsive to dispute, is a way to ensure they respect human rights to autonomy and dignity. We investigate the design of public urban AI systems for contestability through the example of camera cars: human-driven vehicles equipped with image sensors. 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. We describe how civic participation faces issues of representation, public AI systems should integrate with existing democratic practices, and cities must expand capacities for responsible AI development and operation.