John Calvin Commentary Deuteronomy 19:16

"If an unrighteous witness rise up against any man to testify against him of wrong-doing," — Deuteronomy 19:16 (ASV)

If a false witness rise up against any man. Because the fear of God does not so prevail in all people that they voluntarily abstain from the love of slander, God here appoints the punishment for perjury: for political laws are enacted against the ungodly and disobedient, so that those who despise God’s judgment might be brought before human tribunals.

Although perjury is not here ordained to be tried before the judges unless there is an accuser who complains that he has been unjustly injured by false witness, still reason dictates that if anyone has been condemned to death by false witnesses, the judges should not hesitate to officially investigate the matter. Yet, since people are generally inclined to assert their own innocence, God has deemed it sufficient to state that if any complaint is lodged, the judges should diligently investigate it, and if the crime is proved, should inflict the punishment of retaliation (talionis).

Thus it appears that false witnesses and murderers stand in the same light before God. By commanding that the inquiry should be made not only by the judges, but also by the priests, as if God Himself were present, He shows that He requires unusual diligence, because a secret crime is not easily detected without the most meticulous care.