"We have detained four persons in connection with the case and and have conducted DNA tests on them. The test reports are awaited," Mumbai Police Commissioner Satyapal Singh told reporters here today.
Those detained are auto and taxi drivers and some of them have criminal antecedents, he added.
Three police teams have been formed and with the help of her mobile phone call data record, the victim's last known location has been traced, Singh added.
The partially decomposed body of Esther was found near the Eastern Express Highway in central Mumbai last week.
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Esther had landed in Mumbai on January 4 after taking a train back to the city from her native place in Andhra Pradesh.
The girl, who has been employed in a software company in the city, was reported missing the next day. Police had said that the girl was allegedly sexually assaulted and later killed.
Police said they have already sent Esther's T-shirt for a forensic test to trace any foreign DNA.