Impeachment is analogous to indictment in regular court proceedings; trial by the other house is analogous to the trial before judge and jury in regular courts. Typically, the lower house of the legislature impeaches the official and the upper house conducts the trial.
At the federal level of government, agencies such as the U.S. Department of Justice's Civil Rights Division, the U.S. Department of Education's Office for Civil Rights, and the Equal Employment Opportunity Commission (EEOC) investigate claims of civil rights violations and discrimination.
These provisions and other civil rights laws are enforced by a number of federal agencies, including the Department of Justice (DOJ), the Department of Education (ED), the Department of Labor, the Equal Employment Opportunity Commission (EEOC), the Department of Health and Human Services, and others.