The Jewish leaders decided to involve the Romans in Jesus's execution and sent Jesus to Pontius Pilate, the Roman governor.
MK 15:1-5 "Early in the morning the chief Priests met hurriedly with the elders, the teachers of the Law, and the whole Council, and made their plans. They put Jesus in chains, led him away, and handed him over to Pilate. Pilate questioned him, `Are you the king of the Jews?' Jesus answered, `So you say.' The chief priests were accusing Jesus of many things, so Pilate questioned him again, `Aren't you going to answer? Listen to all their accusations!' Again, Jesus refused to say a word, and Pilate was amazed."
Comment: It is unclear whether the Jewish leaders at the exact time of Jesus's trial had the authority to execute someone. In John's gospel, when Pilate tells the Jewish leaders to try Jesus according to their own law, they respond "We are not allowed to put anyone to death (JH 18:31)." However, they seem to have this authority during Jesus's lifetime (see the story of the woman "caught in adultery" whom the Jews wanted to stone to death in JH 8: 1-11) and immediately after Jesus's life (they stone to death Stephen, the first Christian martyr, in Acts 7:54-60).