He wasn't reincarnated, he rose from the dead. His body was gone because it just got up and left. He was murdered, he was crucified. That is murder.
Pontius Pilate left the decision to the crowd, who were influenced by the enemies of christ, and some were on their payroll.
Many books have explored the responsibilty of Pilate for Jesus's death, even the Bible (Matthew) tells of Pilate's reluctance in sending him to his death. I did a paper on it.