Assessment of the Indian Health Service Act of 2019 This bill requires the Department of Health and Human Services to contract with private entities to assess the health care delivery systems and financial management of the Indian Health Service. The assessment must cover a variety of areas, including the demographics and health care needs of the patient population, health care capabilities and resources, staffing levels at medical facilities and the productivity of each health care provider, information technology strategies related to providing health care, business processes, the competency of leadership regarding specified issues, tracking patients eligible for other federal health care programs, and the number of procurement contracts and awards under the Buy Indian Act.