Refund to Rainy Day Savings Act This bill requires the Department of the Treasury to establish and implement a Refund to Rainy Day Savings Program to permit a taxpayer to defer payment on 20% of a tax refund to be deposited into a Treasury account, accumulate interest, and disbursed to the taxpayer in six months. The bill also amends the Assets for Independence Act to reauthorize the Assets for Independence (AFI) federal matched savings program through FY2023 and require appropriations for the program to be reserved for: general research and evaluation, grants for AFI innovation projects to expand the availability of matched savings accounts to low-income individuals, and a three-year pilot program to evaluate savings matches for low-income taxpayers. The Department of Health and Human Services (HHS) must establish a three-year matched savings account pilot program to encourage savings by low-income taxpayers. Under the program, HHS may provide grants to qualified entities to match funds saved by low-income taxpayers under the Refund to Rainy Day Savings Program. Qualified entities for the pilot program include: nonprofit organizations, state or local government agencies or tribal governments applying with a nonprofit organization, sites that offer free tax assistance under certain Internal Revenue Service programs, and low-income credit unions and community development financial institutions that work with a local community-based organization to address poverty and the needs of community members for economic independence and stability. HHS must: (1) contract with an independent research organization to evaluate the pilot program, and (2) report annually to Congress on the progress and outcomes of the pilot program.