Matthew 27:24

So when Pilate saw that he prevailed nothing, but rather that a tumult was arising, he took water, and washed his hands before the multitude, saying, I am innocent of the blood of this righteous man, see ye to it.

Dramatic as that gesture was, it was meaningless. It was still Pilate's hand that must sign the death warrant, washing or no washing. Robertson said:

Pilate, of course, could not escape the full legal and moral responsibility for his cowardly surrender to the Sanhedrin. The guilt of the Sanhedrin (both Pharisees and Sadducees unite in the demand for the blood of Jesus) is beyond dispute. It is impossible to make a mere political issue out of it and lay the blame on the Sadducees, who feared a revolution. The Pharisees began the attacks on Jesus on theological and ecclesiastical grounds. The Sadducees later joined the conspiracy against Christ. Judas was a mere tool of the Sanhedrin, who had his resentments and grievances to avenge. There is guilt enough for all the plotters in the greatest wrong of the ages.[3]

Futile as Pilate's gesture was, it served the Christian gospel by reaffirming the righteousness and innocence of Christ. Thus, God caused the wrath of man to praise him (Psalms 76:10).