COVID-19 Emergency Housing Relief Act of 2020 This bill suspends certain requirements for federally assisted public housing residents and prohibits termination of available low-income housing choice vouchers during the COVID-19 (i.e., coronavirus disease 2019) public health emergency period. Specifically, the bill suspends (1) community service requirements, (2) any work requirement or time limitation established in connection with the Moving to Work demonstration program, (3) the minimum rental amount families are required to pay, and (4) the requirement that a family not be absent from a unit for more than 180 consecutive calendar days. These suspensions last until six months after the end of the COVID-19 public health emergency period. Additionally, during the COVID-19 public health emergency period, and for 60 days thereafter, public housing agencies may not terminate available low-income housing choice vouchers for the failure to enter into a lease.