The short answer is No! Do not do it! The police would like nothing better than to wrap up their investigation with telling admissions from the person accused of a crime, and will try and convince you that it is in your best interest to tell your side of the story. That may or may not be true, but there is no way for you to be sure unless you first hire an experienced criminal defense lawyer to discuss your situation in private. Despite what the officers tell you, you can always go back AFTER getting legal advice to set the record straight. Often people explain what they think is a valid defense, but the lawyer finds himself boxed in by the statement and how it might differ from physical evidence in the case. The safest approach, short of explaining how you were in Canada when the crime took place, is to remain silent until you get more information about what the police are investigating.