Choose Home Care Act of 2021 This bill provides for coverage of home-based extended care services under Medicare. Specifically, the bill provides for coverage of services that are furnished to Medicare beneficiaries in their homes by home health agencies, including nursing care, meals and nutritional support, home medical supplies, nonemergency medical transportation, and care coordination. Coverage includes 30 days of post-hospital care and other periods of extended illness, as determined by the Centers for Medicare & Medicaid Services (CMS). Home health agencies that provide such services may receive additional payments in accordance with a specified methodology. The CMS may make payments for covered services furnished before 2022 during any period in which there is a public health emergency.