Out-of-distribution (OOD) detection is crucial for the deployment of machine learning models in the open world. While existing OOD detectors are effective in identifying OOD samples that deviate significantly from in-distribution (ID) data, they often come with trade-offs. For instance, deep OOD detectors usually suffer from high computational costs, require tuning hyperparameters, and have limited interpretability, whereas traditional OOD detectors may have a low accuracy on large high-dimensional datasets. To address these limitations, we propose a novel effective OOD detection approach that employs an overlap index (OI)-based confidence score function to evaluate the likelihood of a given input belonging to the same distribution as the available ID samples. The proposed OI-based confidence score function is non-parametric, lightweight, and easy to interpret, hence providing strong flexibility and generality. Extensive empirical evaluations indicate that our OI-based OOD detector is competitive with state-of-the-art OOD detectors in terms of detection accuracy on a wide range of datasets while requiring less computation and memory costs. Lastly, we show that the proposed OI-based confidence score function inherits nice properties from OI (e.g., insensitivity to small distributional variations and robustness against Huber $ε$-contamination) and is a versatile tool for estimating OI and model accuracy in specific contexts.