The ongoing COVID-19 pandemic, caused by the highly contagious SARS-CoV-2 virus, has overwhelmed healthcare systems worldwide, putting medical professionals at a high risk of getting infected themselves due to a global shortage of personal protective equipment. This has in-turn led to understaffed hospitals unable to handle new patient influx. To help alleviate these problems, we design and develop a contactless patient positioning system that can enable scanning patients in a completely remote and contactless fashion. Our key design objective is to reduce the physical contact time with a patient as much as possible, which we achieve with our contactless workflow. Our system comprises automated calibration, positioning, and multi-view synthesis components that enable patient scan without physical proximity. Our calibration routine ensures system calibration at all times and can be executed without any manual intervention. Our patient positioning routine comprises a novel robust dynamic fusion (RDF) algorithm for accurate 3D patient body modeling. With its multi-modal inference capability, RDF can be trained once and used across different applications (without retraining) having various sensor choices, a key feature to enable system deployment at scale. Our multi-view synthesizer ensures multi-view positioning visualization for the technician to verify positioning accuracy prior to initiating the patient scan. We conduct extensive experiments with publicly available and proprietary datasets to demonstrate efficacy. Our system has already been used, and had a positive impact on, hospitals and technicians on the front lines of the COVID-19 pandemic, and we expect to see its use increase substantially globally.