Young Witness Assistance Act of 2001 - Authorizes the Director of the Bureau of Justice Assistance to make grants to State and local prosecutors and law enforcement agencies in support of juvenile (17 years of age or younger) and young adult (between 18 and 21 years of age) witness assistance programs. Authorizes grant funds to be used, among other things, for: (1) counseling services to young witnesses of a violent crime; and (2) protective services for young witnesses and their families when a serious threat of harm is made from perpetrators or their associates.