Vaccine Safety Study Act This bill requires the National Institutes of Health (NIH) to conduct or support a study to: (1) compare total health outcomes, including the incidence and risk of autism, between vaccinated and unvaccinated U.S. populations; and (2) determine whether exposure to vaccines or vaccine components is associated with autism spectrum disorders, chronic conditions, or other neurological conditions. The NIH must: (1) seek to include in the study populations that have traditionally remained unvaccinated for religious or other reasons, and (2) ensure the preservation of all data collected or used for the study to facilitate further research by the NIH or others.