Teleradiology applications and universal availability of patient records using web-based technology are rapidly gaining importance. Consequently, digital medical image security has become an important issue when images and their pertinent patient information are transmitted across public networks, such as the Internet. Health mandates such as the Health Insurance Portability and Accountability Act require healthcare providers to adhere to security measures in order to protect sensitive patient information. This paper presents a fully reversible, dual-layer watermarking scheme with tamper detection capability for medical images. The scheme utilizes concepts of public-key cryptography and reversible data-hiding technique. The scheme was tested using medical images in DICOM format. The results show that the scheme is able to ensure image authenticity and integrity, and to locate tampered regions in the images.