Comprehensive Breast Reconstruction Act of 2021 This bill provides for Medicare, Medicaid, and private health insurance coverage of certain tattooing services in connection with post-mastectomy breast reconstruction, and aligns the scope of Medicare and Medicaid coverage of such breast reconstruction with that of private health insurance. Specifically, the bill provides for coverage of reconstructive tattooing services that are performed by a health care practitioner or state-licensed tattoo artist pursuant to a physician prescription, and expands Medicare and Medicaid coverage to include all stages of reconstruction, surgery to produce a symmetrical appearance, and prostheses and physical complications of mastectomies (e.g., lymphedemas).