Sickle Cell Disease Comprehensive Care Act This bill establishes and provides funds for a demonstration project for state Medicaid programs to improve outpatient care for individuals with sickle cell disease, with a focus on young adults and pregnant women. The Centers for Medicare & Medicaid Services must award planning grants to at least 10 states and must select between 5 and 10 states to participate in the project. Participating states must provide specified services and support for individuals with sickle cell disease, including multidisciplinary care teams, appropriate treatments, mental health services, and specialist services. The bill provides a 100% Federal Medical Assistance Percentage (i.e., federal matching rate) for services provided through the project.