The incident occurred on Sunday afternoon, said Dhaka Metropolitan Police's Deputy Commissioner (DC) (Prosecution) AHM Kamruzzaman.
The fugitive, SI Rezaul Karim, is accused of killing a businessman named 'Faruk' in Kafrul, a Dhaka neighbourhood, in November 2012.
Two other accused, SI Nuruzzaman of the Kafrul police and informer Ratan Babu, were also named in the murder case chargesheet.
Kamruzzaman told bdnews24.com the three faced indictment during Sunday's hearing before the Special Tribunal of judge Akhtaruzzaman.
The court rejected their appeal for bail.
He said Rezaul Karim fled after a while by hoodwinking the guards posted outside the lockup.
According to Karumzzaman, Rezaul told the constable on duty that he was an SI; he had gone inside to use the toilet. When the door was opened, he casually walked out.
While Rezaul fled, Nuruzzaman and Ratan stayed on in the lockup.
Kamruzzaman said a case would be filed in connection with the incident. "Action will be taken against those responsible after an investigation."