The hands of the babies had tags tied to them that read 'B/O Zohra', said a senior police officer. He said the babies were prematurely born and weighed 450 grams.
With just the first name of the babies' mother available, the police have contacted hospitals and nursing homes across the national capital to identify her, he said.
Till now, no hospital or nursing home has identified the mother.
The bodies were found without clothes in a park near the SDM court in Keshvapuram on the morning of June 16. They had been covered with leaves and left in a pit under the tree, the officer said.
He added that the police were informed about the infants following which they were taken to a hospital where doctors declared them brought dead.
The officer said they have registered a case on the charge of concealment of birth by secret disposal of the body, the maximum punishment for which is a term of two years along with a fine.
The officer said that they were probing all angles and were looking into the possibility whether the twins were dumped since they had died after birth.
It is also possible that they might have died after being dumped in the park as they are girls, he said.
They also have not ruled out the possibility of an unwed mother dumping the girls in the park.
The police have preserved the bodies at the mortuary and have taken their DNA samples. Their post-mortem is yet to be conducted, he added.