Coronary artery tortuosity (CAT) is characterized by abnormal curvatures and bends that influence blood flow and pose challenges for clinical interventions. CAT is typically assessed using three-dimensional reconstructions from Coronary Computed Tomography Angiography. However, current evaluation methods mainly rely on qualitative assessment through visual inspection, leading to substantial inter- and intra-observer variability. Moreover, the absence of clinically validated grading thresholds hinders the standardized interpretation of quantitative tortuosity metrics. In this study, we introduce a novel unsupervised approach that leverages geometric and signal processing features to identify tortuosity patterns along the vessel. We developed a multivariate discrete Hidden Markov Model to classify each point along the vessel's centerline into one of three distinct tortuosity levels: absent/low, moderate, or severe. The model utilizes features extracted from the 3D centerline, including curvature and Lempel-Ziv complexity, computed across overlapping sliding windows and encoded using a custom algorithm. A post-processing step further refines classification to ensure clinically meaningful insights. The proposed model demonstrated good agreement with expert annotations, suggesting that it provides a reliable and objective tool for quantifying coronary tortuosity. In addition to CAT detection, the method enables the automated localization of segments with varying degrees of tortuosity along the artery in an explainable manner, thereby enhancing visual assessment and highlighting regions requiring closer clinical attention. Our approach offers a data-driven, reproducible, and interpretable alternative to traditional qualitative assessments of CAT.