Many years ago, I was questioned about an assault on my ex-girlfriend (I had a rock solid alibi; it happened in Christchurch and I was in Australia at the time).
The Police came to my work place and wanted me to accompany them to the Police station. They didn't tell me why, and I know my rights so I said no. One of the two cops said something like "being uncooperative won't help you". I said, something like "I know my rights. If you want me to come with you, you will have to arrest me. Are you arresting me?". They didn't answer immediately, but then the other cop said something like "Why not. If you've done nothing wrong, you have nothing to fear" and I remember exactly what I said next. I laughed and said "I have three words for you... Arthur, Allan, Thomas" (the reader may have to look that one up). I could see the pair of them were not happy with that response, so I quickly said words to the effect that "If you want to interview me, I am happy for you to do so at my home, with my solicitor present". With that, they left and later we arranged the interview over the phone.
Once they realised that my alibi was sound they lost interest in me.
My advice to anyone who gets involved as a suspect or a person of interest with the Police is that
1. You do not have to answer any of their questions
2. You do not have to go with them unless they arrest you