This paper presents a method for annotating question decomposition on complex medical questions. The annotations cover multiple syntactic ways that questions can be decomposed, including separating independent clauses as well as recognizing coordinations and exemplifications. We annotate a corpus of 1,467 multi-sentence consumer health questions about genetic and rare diseases. Furthermore, we label two additional medical-specific annotations: (1) background sentences are annotated with a number of medical categories such as symptoms, treatments, and family history, and (2) the central focus of the complex question (a disease) is marked. We present simple baseline results for automatic classification of these annotations, demonstrating the challenging but important nature of this task.