I have heard of the Bill of Rights, (the first 10 amendments to the U.S. Constitution.)  "The right to remain silent" was an issue in Miranda v. The State of Arizona (US Supreme Court 1966) in applying the 5th Amendment as it relates to the phrase "nor shall be compelled in any criminal case to be a witness against himself."  Miranda case also relied upon and referenced Escobedo v. Illinois (US Supreme Court 1964) in which a distinction was drawn between a general investigation into a crime and the questioning of a suspect in the crime being investigated.  There again the "right to remain silent" was a concern.   We know that the phrase "right to remain silent" like the phrase "separation of church and state" are not found in the U.S. Constitution including the amendments but are derived from case law.  

There is also a whole body of law relating to hindering prosecution, interfering with a peace officer, and concealing evidence.  That too has stood the test of time.