An applicant cannot naturalize if he or she commits murder. The Immigration and Naturalization Service requires that an applicant must disclose all relevant facts, including his or her entire criminal history, regardless of whether the criminal history disqualifies the applicant. Click here to see the Immigration and Naturalization Service's study guide and some example questions. However, if your home country allows you to keep your citizenship after you have naturalized to become a US citizen, in reality you will have two citizenships. Once you are a US citizen, you cannot become a citizen of another country without losing your US citizenship.
Expatriation is the voluntary act of relinquishing one's citizenship.
A U.S. citizen loses her citizenship when she voluntarily performs an act specified in the law with the intention of abandoning her U.S. citizenship.