Local Law Enforcement Enhancement Act of 2001 - Authorizes the Attorney General to provide technical, forensic, prosecutorial, or other assistance in the criminal investigation or prosecution of any crime that: (1) constitutes a crime of violence under Federal law or a felony under State or Indian tribal law; and (2) is motivated by prejudice based on the race, color, religion, national origin, gender, sexual orientation, or disability of the victim or is a violation of the hate crime laws of the State or tribe. Directs the Attorney General to give priority for assistance to crimes committed by offenders who have committed crimes in more than one State and to rural jurisdictions that have difficulty covering the extraordinary investigation or prosecution expenses.Authorizes the Attorney General to award grants to assist State, local, and Indian law enforcement officials with such extraordinary expenses. Directs the Office of Justice Programs to: (1) work closely with funded jurisdictions to ensure that the concerns and needs of all affected parties are addressed; and (2) award grants to State and local programs designed to combat hate crimes committed by juveniles.Prohibits specified offenses involving actual or perceived race, color, religion, national origin, gender, sexual orientation, or disability.Directs the U.S. Sentencing Commission to study and provide sentencing enhancements for adult recruitment of juveniles to commit hate crimes.Amends the Hate Crimes Statistics Act to require the crime data to be collected and published by the Attorney General to include data about crimes that manifest evidence of prejudice based on gender.