"No person...shall be compelled in any criminal case to be a witness against himself." Sound familiar? It's the Fifth Amendment guarantee against self-incrimination - the right to remain silent.
The question is how do you invoke your constitutional right to silence. How do you talk without speaking? [see lyrics from "Sounds of Silence" by Simon and Garfunkel] As of Monday, June 17, 2013, the US Supreme Court has made clear that you cannot simply assert your constitutional right to remain silent by, well, remaining silent. No, you must expressly invoke the right. See Salinas v. State, No. 12-246, 570 U.S. __ (2013).
Salinas originated in Texas - Harris County to be precise. Mr. Salinas was interviewed by the police after a double murder. By all accounts he was at the police station voluntarily and was not in custody. Because he was not in custody the police did not provide Mr. Salinas with his Miranda warnings, one of which is the right to remain silent. Mr. Salinas answered some questions but fell silent when police asked questions about bullet casings. At trial the government argued that Mr. Salinas' silence was evidence of his guilt. He was convicted and sentenced to 20 years in prison. He appealed arguing that his silence in the face of police questioning invoked his constitutional right to remain silent.
Seems logical, right? However, a plurality of the US Supreme Court held that Mr. Salinas' Fifth Amendment claim fails because he did not expressly invoke the privilege against self-incrimination in response to the officer's question. Mr. Salinas did remain silent but that wasn't enough here. According to the US Supreme Court he should have expressly claimed his privilege; he could not simply remain mute. The plurality held that "the Fifth Amendment guarantees that no one may be 'compelled in any criminal case to be a witness against himself;' it does not establish an unqualified 'right to remain silent'".
So, at the very outset, if you find yourself in the unfortunate position of being questioned by the police - be it in a police station or on the side of the road or wherever - the first question to politely ask is "am I free to leave". [Also, it is important to remember that if you are speaking with a police officer, the conversation is being recorded] If the answer to that question is "yes" then it is a very good idea to leave. If the answer to that question is "no" then the response to any question, in light of Salinas, should be "I am invoking my constitutional right to remain silent and I want a lawyer." Then politely remain silent.
What Salinas leaves unanswered, however, is whether the government can use an accused's assertion of the Fifth Amendment during a non-custodial police interview as part of its case in chief. Courts are split on that very issue. I suspect the answer to that question may be yes. We will see...