No Mandates Act This bill prohibits federal agencies and certain entities that receive federal funding from requiring COVID-19 vaccinations. Specifically, federal agencies may not issue rules, regulations, or guidance that require an individual to receive a COVID-19 vaccination. The bill also prohibits requiring a COVID-19 vaccination to access federal property and services or congressional grounds and services. Additionally, an entity that received federal COVID-19 relief funds or receives other federal funds after this bill's enactment may not require a COVID-19 vaccination as a condition of providing any service to an individual.