COVID-19 Emergency Housing Relief Act of 2020 This bill establishes certain flexibilities related to public housing during the COVID-19 (i.e., coronavirus 2019) emergency. For example, the bill suspends work requirements and time limitations on assistance associated with the Move to Work program; suspends the requirement that families residing in public housing must pay a minimum amount in rent; suspends the requirement that families may not be absent from a public housing unit for more than 180 consecutive calendar days; prohibits public housing agencies (PHAs) from terminating a household's eligibility for a housing choice voucher based on the household's failure to enter into a lease for an assisted unit; requires the Department of Housing and Urban Development (HUD) and the Department of Agriculture (USDA) to suspend income reviews, except in certain instances; allows HUD and USDA to suspend or delay certain deadlines relating to PHAs or owners of federally assisted housing; and suspends requirements for owners of federally assisted multifamily housing to remit residual receipts to HUD.