Branch banking continues to depend on relationship knowledge, local customer familiarity and routine operational checks, yet many branches struggle to separate ordinary customer variation from early risk signals that require supervisory attention. This paper develops a practical risk-based customer monitoring framework using statistical classification for branch banking environments. The objective is to show how routine customer, account-conduct and transaction indicators can be converted into low, medium and high monitoring bands that support proportionate branch action. The paper is designed as a methodological and conceptual research article rather than a completed empirical study. It synthesizes credit scoring, behavioral monitoring, anomaly detection, model validation and banking governance literature to propose a branch-level classification architecture. The framework uses structured customer variables, account behavior, product exposure, transaction irregularity, service interaction and branch judgment as inputs to a transparent classifier such as logistic regression, discriminant analysis, decision-tree rules or scorecard-based segmentation. The output is not only a predicted risk label but a management response: routine monitoring, enhanced review, documentary verification, supervisory approval or escalation to risk and compliance teams. The paper contributes by translating statistical classification into a bank-operational monitoring process that can be implemented even by branches with moderate data maturity. It also emphasizes calibration, class imbalance, explainability, override documentation and periodic model review so that customer monitoring remains auditable, fair and useful for managers.