I would agree in general. It was eventually a Rome decision but was handed back.
Luke 23:11-16 English Standard Version
11 And Herod with his soldiers treated him with contempt and mocked him. Then, arraying him in splendid clothing, he sent him back to Pilate. 12 And Herod and Pilate became friends with each other that very day, for before this they had been at enmity with each other.
13 Pilate then called together the chief priests and the rulers and the people, 14 and said to them, “You brought me this man as one who was misleading the people. And after examining him before you, behold, I did not find this man guilty of any of your charges against him. 15 Neither did Herod, for he sent him back to us. Look, nothing deserving death has been done by him. 16 I will therefore punish and release him.”
Matthew 27:24-26 English Standard Version
Pilate Delivers Jesus to Be Crucified
24 So when Pilate saw that he was gaining nothing, but rather that a riot was beginning, he took water and washed his hands before the crowd, saying, “I am innocent of this man’s blood;[a] see to it yourselves.” 25 And all the people answered, “His blood be on us and on our children!” 26 Then he released for them Barabbas, and having scourged[b] Jesus, delivered him to be crucified.
Kinda surprised me that even Mick Jagger noted Pilate washed his hands and (thereby) sealed his (own) fate.
If Jagger wrote that song. I haven’t looked.