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Dialogue state trackers have made significant progress on benchmark datasets, but their generalization capability to novel and realistic scenarios beyond the held-out conversations is less understood. We propose controllable counterfactuals (CoCo) to bridge this gap and evaluate dialogue state tracking (DST) models on novel scenarios, i.e., would the system successfully tackle the request if the user responded differently but still consistently with the dialogue flow? CoCo leverages turn-level belief states as counterfactual conditionals to produce novel conversation scenarios in two steps: (i) counterfactual goal generation at turn-level by dropping and adding slots followed by replacing slot values, (ii) counterfactual conversation generation that is conditioned on (i) and consistent with the dialogue flow. Evaluating state-of-the-art DST models on MultiWOZ dataset with CoCo-generated counterfactuals results in a significant performance drop of up to 30.8% (from 49.4% to 18.6%) in absolute joint goal accuracy. In comparison, widely used techniques like paraphrasing only affect the accuracy by at most 2%. Human evaluations show that COCO-generated conversations perfectly reflect the underlying user goal with more than 95% accuracy and are as human-like as the original conversations, further strengthening its reliability and promise to be adopted as part of the robustness evaluation of DST models.