In the Gospels, Pontius Pilate finds no real guilt in what Jesus has done, but he reluctantly hands Jesus over to the local authorities to do with Jesus as they see fit. In the Gospel of Matthew, Pilate famously "washes his hands" indicating that Jesus' fate is no longer his responsibility.
In The Crucible, Herrick and the authorities of the court come to collect Elizabeth on charges: Abigail claims Elizabeth used witchcraft to stab Abigail using a poppet (a practice more popularly known in Voodoo). Elizabeth says she has kept no poppets since she was a girl. They find a poppet which had been planted there by Mary Warren. Herrick and the authorities are not convinced that Elizabeth is innocent and they insist on taking Elizabeth into custody. Hale begins to tell Proctor that if she is innocent, the court will discover it. However, Proctor interrupts him and asks why she is guilty until proven innocent while Abigail and Parris are innocent and not even subjected to proving that alleged innocence:
Why do you never wonder if Parris be innocent, or Abigail? Is the accuser always holy now? Were they born this morning as clean as God's fingers?
Considering the parallel, Elizabeth as Jesus and Hale as Pontius Pilate, the comparison is appropriate. Both Elizabeth and Jesus are innocent; and their accusers are assumed to be innocent from the beginning. Hale and Pilate have some authority, some say in their respective matters, and yet they both (albeit reluctantly) turn their accused citizen over to the local authorities. Just as Pilate found no real guilt in Jesus, Hale has real doubts that Elizabeth is guilty; and as the play goes on, Hale becomes more convinced that all the accusations of witchcraft are false. When Hale consents to allow the local authorities to take Elizabeth, this is comparable to Pilate handing Jesus over the local authorities.