The biblical record is clear that Pilate was reluctant to execute Jesus. Convicted of religious blasphemy by Jewish leaders, the charges actually brought before Pilate were of political insurrection. Crucifixion was a typical punishment for political insurgents. Pilate's allegiance to Caesar could have been questioned had he not rendering a death sentence (John 19:12).
Pilate appears to have invoked Hebrew symbolism by washing his hands (Deuteronomy 21:1-8). If a murdered person was found on your property, by Jewish law, a sacrifice should be made. This included washing of hands, and the proclamation that the blood of the sacrificed animal was not on your hands.
Seemingly, Pilate was indicting the crowd for murdering Jesus with symbolism they would clearly understand (Matt 27:23-25).