Conrad State 30 and Physician Access Reauthorization Act This bill amends the Immigration and Nationality Technical Corrections Act of 1994 to extend the J-1 visa waiver program (Conrad state 30/medical services in underserved areas) through September 30, 2021. The bill sets forth specified employment protections and contract requirements for alien physicians working in underserved areas, including: (1) a six-month status extension for a physician whose application his been denied by an oversubscribed state and who then agrees to work in an undersubscribed state, and (2) an allowable adjustment from a J-1 to an H-1B visa (specialty workers with a permitted U.S. stay of up to six years) for a physician fulfilling waiver requirements. The bill permits a state, under specified circumstances, to recapture a waiver slot lost to another state if a physician working in a health facility accepts employment with such a facility in another state. The number of alien physicians that a state may be allocated is increased from 30 to 35 per fiscal year under specified circumstances. The bill provides for: (1) additional increases or decreases based upon demand, and (2) up to three visa waivers per fiscal year per state for physicians in academic medical centers. Dual intent is permitted for an alien coming to the United States to receive graduate medical education or training or to take examinations required for graduate medical education or training.