Tuberculosis (TB) remains a global health challenge, particularly in resource-constrained settings where advanced diagnostics are scarce. Recent research has explored the potential of using cough signals, combined with clinical data and machine learning (ML), as a non-invasive screening method for TB. However, the effectiveness of such approaches remains highly dependent on the specific ML model employed, including its architecture, training procedure, and preprocessing pipeline. This study aims to quantify the complexity of both metadata and temporal cough signals to improve classification outcomes and ensure greater model generalizability. Cough recordings from 1105 participants (TB-positive and TB-negative) in the CODA-TB dataset were analyzed across two levels: (1) metadata complexity, assessing demographic and clinical variable heterogeneity; and (2) time series complexity, evaluating raw acoustic waveform irregularity. Complexity metrics, including Shannon entropy, Hurst exponent, and Fisher’s discriminant ratio, were computed. Metadata analysis identified fever, weight loss (Cramér’s V > 0.3) and heart rate (Fisher score > 100) as highly discriminative. Time series analysis revealed TB-specific patterns, with a Hurst exponent of 0.72 ± 0.15 indicating persistent behavior and a Higuchi fractal dimension of 1.71 ± 0.24 reflecting signal irregularity. By integrating complexity analysis, this study uncovers intricate cough patterns and supports the development of robust, non-invasive screening tools for resource-limited settings and highlights their potential for broader clinical applications.