It has been suggested that the retinal vasculature alternations are associated with dementia in recent clinical studies, and the eye examination may facilitate the early screening of dementia. Optical Coherence Tomography Angiography (OCTA) has shown its superiority in visualizing superficial vascular complex (SVC), deep vascular complex (DVC), and choriocapillaris, and it has been extensively used in clinical practice. However, the information in OCTA is far from fully mined by existing methods, which straightforwardly analyze the multiple projections of OCTA by average or concatenation. These methods do not take into account the relationship between multiple projections. Accordingly, a Multi-projection Consistency and complementarity Learning Network (MUCO-Net) is proposed in this paper to explore the diagnosis of dementia based on OCTA. Firstly, a consistency and complementarity attention (CsCp) module is developed to understand the complex relationships among various projections. Then, a cross-view fusion (CVF) module is introduced to combine the multi-scale features from the CsCp. In addition, the number of input flows of the proposed modules is flexible to boost the interactions across the features from different projections. In the experiment, MUCO-Net is implemented on two OCTA datasets to screen for dementia and diagnose fundus diseases. The effectiveness of MUCO-Net is demonstrated by its superior performance to state-of-the-art methods.