While Large Language Models (LLMs) have emerged as powerful foundational models to solve a variety of tasks, they have also been shown to be prone to hallucinations, i.e., generating responses that sound confident but are actually incorrect or even nonsensical. Existing hallucination detectors propose a wide range of empirical scoring rules, but their performance varies across models and datasets, and it is hard to determine which ones to rely on in practice or to treat as a reliable detector. In this work, we formulate the problem of detecting hallucinations as a hypothesis testing problem and draw parallels with the problem of out-of-distribution detection in machine learning models. We then propose a multiple-testing-inspired method that systematically aggregates multiple evaluation scores via conformal p-values, enabling calibrated detection with controlled false alarm rate. Extensive experiments across diverse models and datasets validate the robustness of our approach against state-of-the-art methods.