Vasantha, an accountant at the Kalasalingam University, Srivilliputhur, in Virudhunagar district had sent the mail from a fictitious id, SP Najmal Hooda said.
Her objective was to take revenge on her husband from whom she separated recently, the officer said.
The email was sent on May 9 around 4 pm from her office computer. The mail stated that she and her husband Natchimuthu were responsible for the 'Mumbai bomb blast', the SP said.
"Now we are going to kill Tamil Nadu CM. We are going to plant bombs in Meenakshi Temple and Andal temple. Can you catch us?" the mail said.
The mail was sent to police email ids as well as to the DSP, Virudhunagar. An FIR has been filed, the official said.
She has been traced but not yet arrested, Hooda said.
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Vasantha, a commerce and management graduate, married Nachimuthu two years ago but the couple separated recently. She has been working at the university since July 2011, police added. Nachimuthu is working in a pharma company at Thane in Maharashtra.
She had also mentioned his phone number in the mail but police said they could not contact him.
Searches were carried out at the Chief Minister's Poes Garden residence at Chennai yesterday, Meenakshi Amman Temple in Madurai and Andal Temple in Srivilliputhur on night of May9 following the threat, police had said.
Following the search at the Chief Minister's residence, they said the email threat turned out to be a hoax.
Police had said a search was conducted at the Meenakshi Temple after a caller had claimed a bomb would go off when the two-day BJP conference was on from May 10.