If you are going to invoke your right to remain silent, STFU from the very beginning.
But you have the right to cease answering questions at any time. Was this one question in a series of questions, several before and several after?
Once he refused to answer, the police were supposed to stop talking to him.
But yes, NEVER talk to the police. If they’ve decided you did it, you aren’t gonna talk em out of it. You’re going to jail either way.
Paging Lois Lerner.