I recently answered this question on Avvo.com. The answer is that law enforcement may arrest you in that situation if they have “probable cause” that a crime was committed and probable cause that you committed that crime.
Probable cause is not an easy term to define. The Oxford Companion to American Law defines probable cause as “information sufficient to warrant a prudent person’s belief that the wanted individual had committed a crime (for an arrest warrant) or that evidence of a crime or contraband would be found in a search (for a search warrant)”. “Probable cause” is a stronger standard of evidence than a “reasonable suspicion”, but weaker than what is required to secure a criminal conviction (proof beyond a reasonable doubt). If law enforcement lacks the necessary probable cause, then you may not be arrested for merely asserting your constitutional right to remain silent and not speak with them.
However, there may be times in which it is advantageous to speak with law enforcement. In those situations, it is always advisable to first hire an experienced criminal defense attorney and weigh your options, rather than go at it alone. Such an attorney can assess the gravity of the situation and advise the best course of action. There is no clear “cookie-cutter” approach that works in all situations. In one situation, it may be advantageous not to make any statements; in another, a detailed explanation may be necessary.
Keep in mind that when you speak with a law enforcement officer, any statement may be used against you. Sometimes a statement may be taken out of context. Sometimes a law enforcement officer may claim that you made a statement that you insist you never stated. Getting an experienced criminal defense attorney may help prevent this from occurring. For one, statements made by an attorney are not considered statements made by you and are not admissible in court. Secondly, an attorney can insist on being present during an interview with law enforcement and take steps to ensure that your answers are properly recorded and/or documented.