Commitment to Veteran Support and Outreach Act This bill authorizes the Department of Veterans Affairs (VA) to provide grants to states to implement programs that improve outreach and assistance to veterans and their families to ensure that such individuals are fully informed about veterans' benefits and programs. Specifically, the VA may provide grants to states to (1) implement or enhance outreach activities or activities to assist in the development and submittal of claims for veterans, or (2) increase the number of county or tribal veterans service officers in the state. The VA must prioritize awarding grants in areas with a critical shortage of county or tribal veterans service officers, areas with high rates of suicide among veterans, and areas with high rates of referrals to the Veterans Crisis Line.