Veteran Urgent Access to Mental Healthcare Act (Sec. 2) This bill directs the Department of Veterans Affairs (VA) to furnish to former members of the Armed Forces: (1) an initial mental health assessment; and (2) the mental health care services required to treat the member's urgent mental health care needs, including risk of suicide or harming others. A former member of the Armed Forces is an individual who: served in the active military, naval, or air service, was discharged or released under a condition less than honorable (except a dishonorable or bad conduct discharge), has applied for a character of service determination that has not yet been made, and is not otherwise eligible to enroll in the VA health care system by reason of such discharge or release; or while serving in the Armed Forces, was deployed in a theater of combat operations or an area at a time during which hostilities occurred in that area, participated in or experienced such combat operations or hostilities (including by controlling an unmanned aerial vehicle from a location other than such theater or area), or was the victim of a physical assault of a sexual nature, battery of a sexual nature, or sexual harassment. The VA may provide such mental health care services at a non-VA facility if: (1) the receipt of mental health care services by an individual in VA facilities would be clinically inadvisable, or (2) VA facilities are not capable of furnishing such mental health care services to that individual economically because of geographical inaccessibility. The VA shall: (1) seek to ensure that such mental health care services are furnished in a therapeutically appropriate setting, and (2) provide referral services to assist former members who are not eligible for such VA services in obtaining services from non-VA sources. (Sec. 3) The VA shall establish a process by which an individual who was discharged from the Armed Forces can seek a VA determination as to whether the discharge was under a condition barring the individual from receiving a VA benefit. If the VA determines that the individual is so barred, the VA shall provide such individual with information regarding his or her ability to address such condition.