The Shroud of Turin is a piece of cloth that has been radio carbon dated to the 14th Century CE. Dramatic claims have been made for this cloth that believers maintain was the actual shroud of Jesus. The Roman Catholic Church owns this cloth and decides which scientists have access to it. Unsurprisingly those scientists the Roman Catholic Church chooses to investigate the cloth generally find results that the Roman Catholics like, the radio carbon dating being an exception.
Scientifically minded people should not be impressed by this piece of linen unless truly independent scientists chosen, for example by Richard Dawkins are allowed access to the cloth. If there is nothing to hide why does the church not allow such independent investigation?