If you are being investigated for committing a crime, you have the right to remain silent under 5th Amendment to the U.S. constitution... And you should invoke that right as soon as you are either (1) being investigated for a crime or (2) arrested for a crime. When being interrogated and detained by the police, many times they are looking to incriminate you! Your best defense is to remain silent or respectfully explain that you do not wish to answer any questions without your lawyer present!