The incident took place in the early hours of Tuesday and one inmate was later found at the Railway station here yesterday, the police said.
The inmate is being counselled in an effort to obtain information on how the plan to run away was made, an official said.
Efforts are on to trace the rest 11 children, the police added.
The district Child Welfare Committee(CWC) today sought a report from it about the incident, CWC member Benudhar Senapati said.
Underlining the need for proper counselling of the children in the home, Senapati said shortcomings and weaknesses, if any, would be thoroughly examined before working out an action plan for future.
Khurda district authorities are also looking into the episode, the official said.