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Optical Coherence Tomography Angiography (OCT-A) is a non-invasive imaging technique, and has been increasingly used to image the retinal vasculature at capillary level resolution. However, automated segmentation of retinal vessels in OCT-A has been under-studied due to various challenges such as low capillary visibility and high vessel complexity, despite its significance in understanding many eye-related diseases. In addition, there is no publicly available OCT-A dataset with manually graded vessels for training and validation. To address these issues, for the first time in the field of retinal image analysis we construct a dedicated Retinal OCT-A SEgmentation dataset (ROSE), which consists of 229 OCT-A images with vessel annotations at either centerline-level or pixel level. This dataset has been released for public access to assist researchers in the community in undertaking research in related topics. Secondly, we propose a novel Split-based Coarse-to-Fine vessel segmentation network (SCF-Net), with the ability to detect thick and thin vessels separately. In the SCF-Net, a split-based coarse segmentation (SCS) module is first introduced to produce a preliminary confidence map of vessels, and a split-based refinement (SRN) module is then used to optimize the shape/contour of the retinal microvasculature. Thirdly, we perform a thorough evaluation of the state-of-the-art vessel segmentation models and our SCF-Net on the proposed ROSE dataset. The experimental results demonstrate that our SCF-Net yields better vessel segmentation performance in OCT-A than both traditional methods and other deep learning methods.