<p>We propose a novel method for conducting statistical inference on the similarity between two time-series by considering a hypothesis test on the Dynamic Time Warping (DTW) distance. The key strength of the proposed method lies in its ability to control the probability of false detection rate in high-stakes decision-making scenarios when the DTW distance is used. Compared to the literature, we presents a unique challenge in conducing a statistical inference on the DTW distance for controlling the false detection rate. We overcome the challenge by leveraging the concept of Selective Inference. Specifically, we carefully examine the computation process of the DTW distance whose operations can be characterized by quadratic inequalities, and prove that a satisfactory inference on the DTW distance is indeed possible. Experiments conducted on both synthetic and real-world datasets robustly support our theoretical results, showcasing the superior performance of the proposed method.</p>