Scientists in the '80s did carbon dating and are certain that it could not have existed before the Middle Ages, but they can't agree on a convincing explanation of how it was created. Apparently some sort of radiation was involved, but it's not likely that there was a radioactive corpse.
Here's a possibility nobody has considered; what if the cloth had been placed over a statue of Jesus Christ that was carved from some sort of radioactive material? That doesn't explain the blood on the Shroud, but it's not impossible that whoever authorized the creation of the statue might have added human blood to make it look authentic and impress people. (Hmmm... Maybe that would make a good plot idea. Too bad I don't write that sort of books.)
A lot of people in the Catholic Church believe that the Shroud of Turin actually was the burial cloth of Jesus Christ. But it doesn't take scientific evidence to make the authenticity of the Shroud doubtful. According to the Bible, Jesus was buried in two separate cloths, one on his head and one on his body. The Shroud of Turin is only one piece of cloth.
However all Christians can be inspired by the reminder it gives of the Crucifixion. I hope my book will also be an inspiration to the kids who read it.