The allegation, however, was denied by the ruling AIADMK (Amma).
Dharmapuri District Child Welfare officer J Raja Meenakshi filed the complaint with the City Police alleging that the minister had demanded Rs 20 lakh for her transfer to Chennai.
The complaint said she was appointed during the reign of late chief minister J Jayalalithaa and she was "doing well" in her job. Subsequently, the minister, she claimed, made a demand of Rs 10 lakh to allow her to "continue in her job". She alleged she was intimidated and she had to pay the said amount to the minister.
She claimed she has forwarded the complaint to Chief Minister K Palaniswami's office, Director General of Police T K Rajendran, Leader of Opposition and DMK working president M K Stalin.
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Speaking to reporters, she alleged that the minister and her husband had allegedly "threatened" her on the issue.
The officer claimed to have audio and video evidence to back her claim.
She claimed the police informed her that her complaint will be "referred to the vigilance department".
The ruling party sources said the minister is expected to make a statement soon after "concluding discussions" with senior leaders.
Saroja facing graft allegations comes against the backdrop of recent raids by I T department against Health Minister C Vijayabaskar.
DMK leader Stalin called for the sacking of Saroja.
"Palaniswami should immediately sack Saroja and constitute a probe against her," he said in a statement.
CPI(M) state secretary G Ramakrishnan, who also demanded a probe into the allegations, said an appropriate action be taken against the minister.
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