Classified Veterans Access to Care Act - Requires the Secretary of Veterans Affairs (VA) to: (1) establish standards and procedures to ensure that a veteran who participated in a classified mission or served in a sensitive unit while in the Armed Forces may access mental health care provided by the VA in a manner that fully accommodates the veteran's obligation to not improperly disclose classified information; (2) disseminate guidance to employees of the Veterans Health Administration, including mental health professionals, on such standards and procedures and on how to best engage such veterans during the course of mental health treatment with respect to classified information; and (3) ensure that an individual may elect to identify as such a veteran on an appropriate form.