If an individual is being detained or has been arrested, one does not have a legal obligation to answer any questions and can request legal representation before answering or talking to anyone. One must specifically request an attorney, and must clearly and without equivocation invoke their right to remain silent. Although, if you refuse to answer questions, a police officer may still arrest you. However, it should be noted he would have likely done so regardless.
The right to remain silent remains and does not end until you have adequate and proper legal representation.