It is a relatively well-known trope that if the police arrest you, you have the right to remain silent. This right is directly in the Miranda Rights. However, a very little known case in 2013 that went to the Supreme Court now makes it a bad idea to actively invoke the 5th Amendment. It is also a bad idea to give any information to the police, even if they are not accusing you of a crime and are just asking for information. Thanks to the Supreme Court case Salinas vs. Texas, it is no longer a good idea to talk to the police at all about anything.
What was Salinas vs. Texas?
In this case, an arrested gentleman was talking directly to the police, answering what seemed to be innocuous questions. However, when the individual realized that the questions were becoming more pointed, he went silent.
The end result of the resulting Supreme Court case is that prosecutors are now allowed to tell juries that an individual invoked the 5th Amendment at the time of his or her arrest. This can make that person look guilty, even though invoking the 5th is not an admission of guilt.
What do I say to the police?
You are legally obligated to tell the police your name and what you are doing if a police officer asks for it. Beyond this, even if you are not being arrested, your next (and only) words to the police should be, “I want a lawyer.”
Doing otherwise could put you at serious risk. The police officer could misremember what you were saying at the time, or the police may interpret any slight inconsistencies in your story as lies.