COVID-19 Racial and Ethnic Disparities Task Force Act of 2020 This bill establishes the COVID-19 Racial and Ethnic Disparities Task Force within the Department of Health and Human Services and sets forth its duties and membership. The task force must provide reports and recommendations related to racial and ethnic disparities in the COVID-19 (i.e., coronavirus disease 2019) response to Congress and relevant federal agencies. First, the task force must report weekly on COVID-19 infections and patient outcomes with data disaggregated by race and ethnicity. The reports must also identify communities with high levels of racial and ethnic disparities in COVID-19 measures and recommend how to allocate health care and other resources to address these disparities. Second, the task force must report biweekly on the disbursement of federal COVID-19 relief funds and how to use any undisbursed funds to address racial and ethnic disparities. Lastly, the task force must submit a final report that describes factors that contributed to racial and ethnic disparities with respect to the COVID-19 pandemic, with recommendations to address them in responses to future infectious disease outbreaks. The task force terminates 90 days after the end of the COVID-19 public health emergency . However, the bill permanently establishes a successor task force to address racial and ethnic disparities during future public health emergencies.