Without Probable Cause to search your car or your home the Police must have your consent. You have the Constitutional Right to refuse to give permission for the Police to search.
Sometimes when "consent" is given to search your car or to search your home, the Police come upon some contraband which you did not even know was present. It may have belonged to a prior passenger or to some visitor in your home. The Police will charge you with this violation.
Since most requests for car searches are done on the highway while the Police are videotaping the stop, it is difficult for the Police to "remember" the facts any differently than shown on the Police video. The refusal of consent is an exercise of your Constitutional Rights and the video will show your refusal.