Care for Veterans Act of 2019 This bill requires hospital care and medical services to be furnished to veterans and reservists who were exposed to volatile organic compounds, including trichloroethylene and benzene, while serving at Wurtsmith Air Force Base in Oscoda, Michigan. Family members of veterans and reservists who resided at Wurtsmith Air Force Base are also eligible for hospital care and medical services under this bill. The bill also provides a presumption of service connection for veterans and reservists who were exposed to volatile organic compounds while serving at Wurtsmith Air Force Base. Under a presumption of service connection, specific conditions diagnosed in certain veterans are presumed to have been caused by the circumstances of their military service. Health care benefits and disability compensation may then be awarded.