In the NIV, the first part of v. 37 is a declaration by Pilate: "You are a king, then!" In the NRSV (and my Greek text) it is a question: "So you are a king?"

In some ways, this is another wrong question. Jesus turns it around: "You are saying that I am a king." With that statement is Jesus again putting Pilate on trial: "You have said it, but is it what you believe?"

Here is a story that illustrates what is going on in this dialogue between Jesus and Pilate: An Amish man was once asked by an enthusiastic young evangelist whether he had been saved, and whether he had accepted Jesus Christ as his Lord and Savior? The gentleman replied, "Why do you ask me such a thing? I could tell you anything. Here are the names of my banker, my grocer, and my farm hands. Ask them if I've been saved."

Jesus could tell Pilate anything. What is important is what Pilate believes.