Safe Testing at Residence Telehealth Act of 2021 This bill provides for Medicare payment of certain at-home diagnostic tests and telehealth assessments that are provided in relation to COVID-19 (i.e., coronavirus disease 2019). Specifically, during the public health emergency, the bill requires Medicare payment of diagnostic tests for respiratory conditions other than COVID-19 (e.g., influenza) that are used to finalize a COVID-19 diagnosis and of COVID-19 blood tests that are ordered via telehealth, as well as for related telehealth assessments, regardless of whether the practitioner who orders the test is the one who furnishes it and regardless of the location of the practitioner. The bill requires practitioners to report specified demographic data with respect to such tests and services in order to receive payment, and prohibits payment for in-person tests that were already ordered via telehealth.