Your right to remain silent and not answer any questions without the presence of legal counsel is entirely dependent on your ability to remain calm during a very tense, stressful situation.  The right to remain silent comes from the 5th Amendment to the United States Constitution and was made famous by a case that started right here in Arizona, Miranda v. Arizona.  You can simply not answer questions and remain silent, or you can inform law enforcement you are exercising your right to remain silent under the 5th Amendment of the United States Constitution.