Community-Based Response Act of 2021 This bill establishes a program to assist communities with implementing alternative emergency response models in vulnerable populations to resolve crisis situations that may not require a law enforcement response or situations in which a law enforcement response may increase the risk of harm. Specifically, Administration for Community Living, in consultation with the Department of Housing and Urban Development and the Department of Justice, must award grants to eligible partnerships to establish or expand these models. The partnerships must consist of a unit of local or tribal government that is independent of law enforcement agencies and a nonprofit, community-based organization or consortium of such organizations. The partnerships may also include other entities, such as nonprofit or public institutions of higher education and behavioral health organizations. A partnership may use grant funds for a variety of purposes, such as triaging 9-1-1 calls to refer certain emergencies to entities other than law enforcement. In awarding these grants, the administration must prioritize partnerships that include community-based organizations that have a record of effectively serving, and are led by members of, vulnerable populations.