What level of government or government agency is responsible for dealing with racism? Why?
I'm assuming you mean the American government and, well, there really isn't a level of government or a specific agency that deals with racism, per se. We have a court system and a Justice Department that deal with issues of racial discrimination and hate crimes based on race, but these are actions as opposed to social beliefs.
It is impossible for government to control a person's racism, they can only seek to influence it through education. What's more, racism is not illegal.
Depending on the type of crime and the state in which it happens, some murders and assaults can be considered hate crimes if they can prove the motivation for the crime was race. In that case, we have a judicial system and sometimes US Attorneys will investigate on behalf of the Justice Department, and in other cases, such as during the Civil Rights Era of the 1950s and 1960s, the FBI has been used because states were not acting in accordance with court rulings.