State & Local Emergency Stabilization Fund Act of 2020 This bill appropriates $600 billion in additional funding for states, territories, tribal governments, and local communities due to the COVID-19 (i.e., coronavirus disease 2019) public health emergency and allows additional uses for Coronavirus Relief Fund payments. The bill allows payments under this bill or from the Coronavirus Relief Fund to be used for expenditures from January 1, 2020, to June 30, 2022, regardless of a connection to the COVID-19 emergency. Payments may not be used to provide a tax cut, rebate, or other tax benefit or to reduce or eliminate a fee. The funds provided by this bill are allocated between (1) the U.S. Virgin Islands, Guam, the Northern Mariana Islands, American Samoa; (2) tribal governments; (3) states, the District of Columbia, and Puerto Rico; and (4) local communities. Payment amounts for states, the District of Columbia, and Puerto Rico are based on population and the coronavirus infection rate. The bill sets a minimum payment amount.