These are called your Miranda Rights, from the case of Miranda V. Arizona, and they are derived under the 5th Amendment.The 5th Amendment says, "No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury" which is basically saying that you do not have to admit to anyone if you have committed a crime. The 5th Amendment also goes on to talk about how you cannot be charged with the same crime twice (double jeopardy) and that the government has the right to take your property with fair compensation (eminent domain).
