National Guard and Reservist Suicide Prevention and Community Response Act - Amends the National Defense Authorization Act for Fiscal Year 2008 to require the Department of Defense (DOD) Office for Reintegration Programs, as part of the Yellow Ribbon Reintegration Program, to establish a program to provide National Guard and Reserve members, their families, and their communities with training in suicide prevention and community healing and response to suicide. (Under current law, suicide prevention activities are one category of activities that may be included in the Office's development of outreach services.)