Thats not a problem.

Police dont come asking questions because they want to figure out what happened. They come asking questions because they want to build a case against you. If you refuse to talk, you deny them that.

Watch a true crime series like "The First 48" and you'll see this pattern repeated again and again. The ones who get away with it are the ones who refused to talk from the start.

http://www.kirkpiccione.com/10-reasons-not-talk-police/
https://www.reddit.com/r/MakingaMurderer/comments/3yd11x/dont_talk_to_the_police_a_law_school_professor/