This paper proposes a short-range FMCW radar-based facial authentication and out-of-distribution (OOD) detection framework. Our pipeline jointly estimates the correct classes for the in-distribution (ID) samples and detects the OOD samples to prevent their inaccurate prediction. Our reconstruction-based architecture consists of a main convolutional block with one encoder and multi-decoder configuration, and intermediate linear encoder-decoder parts. Together, these elements form an accurate human face classifier and a robust OOD detector. For our dataset, gathered using a 60 GHz short-range FMCW radar, our network achieves an average classification accuracy of 98.07% in identifying in-distribution human faces. As an OOD detector, it achieves an average Area Under the Receiver Operating Characteristic (AUROC) curve of 98.50% and an average False Positive Rate at 95% True Positive Rate (FPR95) of 6.20%. Also, our extensive experiments show that the proposed approach outperforms previous OOD detectors in terms of common OOD detection metrics.