Purpose: For the cancer in the head and neck (HaN), radiotherapy (RT) represents an important treatment modality. Segmentation of organs-at-risk (OARs) is the starting point of RT planning, however, existing approaches are focused on either computed tomography (CT) or magnetic resonance (MR) images, while multimodal segmentation has not been thoroughly explored yet. We present a dataset of CT and MR images of the same patients with curated reference HaN OAR segmentations for an objective evaluation of segmentation methods. Acquisition and validation methods: The cohort consists of HaN images of 56 patients that underwent both CT and T1-weighted MR imaging for image-guided RT. For each patient, reference segmentations of up to 30 OARs were obtained by experts performing manual pixel-wise image annotation. By maintaining the distribution of patient age and gender, and annotation type, the patients were randomly split into training Set 1 (42 cases or 75%) and test Set 2 (14 cases or 25%). Baseline auto-segmentation results are also provided by training the publicly available deep nnU-Net architecture on Set 1, and evaluating its performance on Set 2. Data format and usage notes: The data are publicly available through an open-access repository under the name HaN-Seg: The Head and Neck Organ-at-Risk CT & MR Segmentation Dataset. Images and reference segmentations are stored in the NRRD file format, where the OAR filenames correspond to the nomenclature recommended by the American Association of Physicists in Medicine, and OAR and demographics information is stored in separate comma-separated value files. Potential applications: The HaN-Seg: The Head and Neck Organ-at-Risk CT & MR Segmentation Challenge is launched in parallel with the dataset release to promote the development of automated techniques for OAR segmentation in the HaN. Other potential applications include out-of-challenge algorithm development and benchmarking, as well as external validation of the developed algorithms.