PER US LAW a U.S. citizen can not be denied entry into the U.S. EVER. It is a so called "fundamental right"
Beyond that you absolutely have the right to refuse to answer any question asked by law enforcement including CBP. The only time a person (not even a citizen) can be forced to answer questions is when a judge orders he or she to do so, after a determination has been made that his or her 5th amendment rights have not been violated.