Rural Health Clinic Burden Reduction Act This bill makes a series of changes to requirements that apply to rural health clinics under Medicare. For example, the bill allows rural health clinics that are not directed by physicians to enter into arrangements with physician assistants or nurse practitioners that generally comply with state laws (regarding scope of practice), rather than other specific requirements. It also specifies that rural health clinics (1) need only have prompt access to clinical laboratory services (as opposed to having to directly provide these services); (2) must be located in a non-urban area with a population that is less than 50,000; (3) may contract with (as opposed to employ) physician assistants or nurse practitioners; and (4) may primarily provide mental health services if located in a designated mental health professional shortage area.