The Police Investigation and Review Commissioner (PIRC) said he would focus on “police actions in efforts to locate” the 16-year-old, who was found dead in the woods from the town of Lanarkshire last Sunday.
Amber was last seen Friday after leaving her home in the Hillhouse area just before 10 p.m.
The alarm was raised on Saturday morning after she failed to return home.
Tragically, police found her body at 10:10 a.m. on Sunday morning in Cadzow Glen, a few feet from where she was last seen the night before.
His brother Connor Gibson, 19, also known as Connor Niven, appeared in court yesterday for his murder.
He is also charged with sexual assault and attempted diversion of the course of justice.
Gibson made no plea at the private hearing at Hamilton Sheriff Court and was remanded into custody.
He should reappear next week.
A Crown Office spokesperson said: “The Crown Office and Procurator Fiscal Service tasked the Police Investigations & Review Commissioner to investigate the circumstances leading to the death of a 16-year-old girl in Hamilton.
A spokesperson for PIRC said: “We are investigating the circumstances that led to the death of a 16-year-old girl in Hamilton.
“Our investigation will focus on the actions of the police in the efforts to locate the girl.
“The matter has been referred to us by the Crown Office and Procurator Fiscal Service and once our investigation is complete, a report on our findings will be submitted to them for review. “
Scottish police said in a statement they would “fully cooperate” with the PIRC investigation.
Meanwhile, Amber’s family paid tribute to the 16-year-old on social media.
Sister Laura Tran said, “We will love you forever, I wish I could protect you. “
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