Immigrants' Mental Health Act of 2021 This bill directs Customs and Border Protection (CBP) to take steps to address mental health issues among immigrants and CBP agents and officers. It also restricts the sharing of mental health information for use in certain immigration proceedings. CBP shall develop training to enable its agents and officers to (1) identify mental health issues and risk factors in immigrants and refugees, (2) provide crisis intervention using a trauma-informed approach, and (3) better manage work-related stress and psychological pressures. CBP shall assign at least one qualified mental or behavioral health expert to each Border Patrol station, port of entry, checkpoint, forward operating base, secondary inspection area, and short-term custody facility. The Department of Health and Human Services may not provide to the Department of Homeland Security information about the mental health of an alien if the information will be used for (1) an asylum determination, (2) an immigration hearing, or (3) a deportation hearing.