Creating Opportunities Now for Necessary and Effective Care Technologies (CONNECT) for Health Act of 2021 or the CONNECT for Health Act of 2021 This bill expands coverage of telehealth services under Medicare. Among other provisions, the bill allows the Centers for Medicare & Medicaid Services (CMS) to waive certain restrictions, such as restrictions on the types of technology that may be used; permanently removes geographic restrictions on originating sites (i.e., the location of the beneficiary) and allows the home of the beneficiary to serve as the originating site for all services; permanently allows federally qualified health centers and rural health clinics to serve as the distant site (i.e., the location of the health care practitioner); and allows the CMS to generally waive coverage restrictions during any public health emergency. Additionally, the CMS must report on the effects of expanded telehealth services during the COVID-19 public health emergency, including with respect to the utilization, quality, and outcomes of services. The Center for Medicare and Medicaid Innovation may also test alternative payment models relating to expanded telehealth services.