An individual who desires fifth amendment protection must say or assert the right to remain silent. Silence is not an invocation of the right to be silent. Salinas v. Texas, 570 U.S. 178, 133 S. Ct. 2174, 2179 (2013); Berghuis v. Thompkins, 560 U.S. 370 (2010); United States v. Monia, 317 U.S. 424, 427 (1943) (if a witness "desires the protection of the privilege, he must claim it or he will not be considered to have been 'compelled' within the meaning of the Amendment"). When an individual does not object, and instead makes damaging disclosures in response to questioning, the privilege is forfeited and there is no later right to object to the use of the statements in a subsequent criminal trial. Rogers v. United States, 340 U.S. 367, 370-71 (1951) (an individual who testifies before a grand jury without claiming the privilege may not later object to the use of incriminating statements against her). The only exception to this rule is if a person is "compelled" to give incriminating testimony. Uniformed Sanitation Men v. Commissioner of Sanitation, 392 U.S. 280, 284-85 (1968) (dismissal of government employees because they had asserted the privilege and refused to testify violates fifth amendment).
For example, a person may claim the privilege by stating, "I refuse to answer on the ground of the fifth and sixth amendment privilege against self-incrimination." Or “I am invoking my right to remain silent and won’t be answering any more questions without a lawyer.” But no precise formula is required:
[i]t is agreed by all that a claim of privilege does not require any special combination of words. . . .
[T]he fact that a witness expresses his intention in vague form is immaterial so long as the claim is sufficiently definite to apprise the [court] of his intention. As everyone agrees, no ritualistic formula is necessary. Quinn v. United States, 349 U.S. 155, 162 (1955), cited in State v. Worgull, 128 Wis.2d 1, 13, 381 N.W.2d 547 (1986).
The Supreme Court has noted that all that is necessary to invoke the privilege is an objection stated in language that can be understood as an attempt to assert the privilege. Quinn v. United States, 349 U.S. 155, 165, 163-65 (1955) (references to "the first and fifth amendment" and "the first amendment to the Constitution, supplemented by the fifth amendment" in refusing to answer questions held sufficient to invoke the privilege's protection). See also Emspak v. United States, 349 U.S. 190, 194 (1955) (statement that refusal to answer was based "primarily [on] the first amendment, supplemented by the fifth" held sufficient to invoke the privilege against self-incrimination).
After saying you are invoking your right to remain silent, SHUT UP! Remain silent. Do not ask any questions of the police or that can be viewed as a waiver of your invoking your right to remain silent. If you are lawfully detained, you can tell the officer your name, address, and date of birth without waiving your rights. The only way to prevent the government from introducing evidence of a suspect's silence at trial is to explicitly invoke (assert) the right to say nothing.
People sometimes ask: “Won’t invoking my right to remain silent make me look guilty.” Maybe, but if your case goes to trial, the jury will never be told that you invoked your rights. In other words, the fact that you remained silent cannot be used against you at trial.