In which language did Pontius Pilate communicate with Jesus? According to this post:


  Both Aramaic and Hebrew were in use in the Land at the time of Jesus. However, while we cannot say one predominated, we can say that Mishnaic Hebrew was very much a living language used by people of all walks of life in Judea and Galilee.


So, maybe we are safe to assume that Jesus spoke these languages. 

Yet, Pontius Pilate was a Roman, who would have spoken Latin. Would he have been able to speak Hebrew? And as such, in the Gospels' account of Pilate's encounter with Jesus, did they speak in Hebrew? Is there any evidence, or perhaps tradition on this?
There is reason to believe that the language Pilate communicated with Jesus was Greek. After all it was the language of commerce at that time throughout the Mediterranean world. Let us not forget that Pilate's inscription on the Title of the Cross was written in Latin, Greek and Hebrew. "This title then read many of the Jews: for the place where Jesus was crucified was near to the city: and it was written in Hebrew, and Greek, and Latin." (John 19:20)  


  How do we know what languages people actually spoke in Roman Judaea? We have a lot of written evidence from the region that is contemporary with the era of Jesus: papyri, inscriptions, graffiti, and historical texts. From hundreds of examples surviving from Roman Judaea, we can easily document which languages people understood and used both in official transactions and in their daily lives. The ancient evidence is very clear on this point: the everyday language spoken by the Jewish and Samaritan populations of Palestine in the time of Jesus was Aramaic, while the official language for administrative communication was Greek.
  
  While Roman soldiers and officials from Rome probably did speak Latin
  among themselves, they would have used Greek to communicate with members of the local ruling class, such as Herod’s family and the Jewish high priests. - Two Archaeologists Comment on The Passion of the Christ


Here is more along this line of thinking.


  In which language did Pilate and Jesus likely converse during Jesus's trial?
  
  Almost certainly in Greek.
  
  The first language of almost all Palestinian Jews in the 1st century was Aramaic. However evidence from the Dead Sea Scrolls, Jewish pseudepigraphic writings, inscriptions on ossuaries (limestone bone burial boxes), etc. show that Greek was spoken there as well. In the Mediterranean world at that time, most people were bilingual (Greek + their native language) so that they could do business with all the other ethnic groups in the Empire.
  
  Jesus grew up in tiny Nazareth where everyone spoke Aramaic, but lived just over the ridge from Sephoris, a large, well-to-do city where Greek was the common language. As a small-time carpenter (Gk., “tekton,” actually more like a craftsman) he would need to speak Greek to snag his share of the business there. Barring a miracle, it wouldn’t have been very cultured or even necessarily grammatically correct, but it would be understandable to another Greek speaker.
  
  Pilate on the other hand, given what we know of him from the Jewish writers Josephus and Philo, most likely would not have put forth the effort to learn Aramaic, the language of a people he had no respect for. Latin was actually not widely spoken at all, being confined mainly to it’s original home Latium. Outside of Rome, it was mainly used for official inscriptions and, occasionally, military orders to fellow Romans.
  
  But he too would have spoken Greek. So, as the scholar Joseph A. Fitzmeyer wrote:
  
  “In what language did Jesus and Pilate converse? There is no mention of an interpreter. Since there is little likelihood that Pilate, a Roman, would have been able to speak either Aramaic or Hebrew, the obvious answer is that Jesus spoke Greek at his trial before Pilate.”