"We will be able to crack this case soon. We are working on different theories. Yesterday, we have sent teams to different locations including neighbouring states," Deputy Inspector General of Police Vimal Gupta told PTI today.
The 39-year-old photographer-turned perfumer was found dead in her rented flat in posh Sangolda village on October 6.
Police suspect that she was raped and murdered somewhere between October 5 afternoon and night, as she had not been in touch with anyone since that time.
Gupta said the woman originally hailed from Nagpur and was married to a photographer Bharat Ramamrutam from Tamil Nadu and was residing at Porvorim near here before she separated from her husband and shifted to Sangolda this year.
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"Police investigations have revealed that she had shifted to Sangolda in July this year and was staying alone," the DIG said.
He said the police are waiting the postmortem report, which would reveal the exact cause of death.
"The maid later informed Monica's brother (Anand, based in Mumbai) who in turn called her husband (Bharat) and then her neighbour, an American woman who had spare keys following which the door was opened and the body was found," he said.
A case has been registered under section 302 (murder) of the IPC.
The perfumer, who was a regular on Goa's social circuit is said to have met Ramamrutham in Mumbai while she was a photographer. She had done her photography course from Mumbai's JJ Institute of Applied Arts.