The woman, identified as Kabita Mahakud, lodged the complaint against the MLA at the Mahila Police station here.
"We have received the complaint and are verifying the matter," Commissioner of Police Y B Khurania told reporters adding DCP Satyabrata Bhoi would monitor the case.
In her FIR, Kabita alleged she was physically and mentally tortured by the MLA and his son-in-law Dinabandhu Barik. Kabita also alleged she was subjected to intimidation.
"I will commit suicide along with my daughter in front of the MLA's house if denied justice," Kabita told reporters.
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Mahakud represents the mineral rich Champua of Keonjhar district in the Assembly and runs a mineral transport company. He defeated the ruling BJD candidate in the last elections.
Mahakud, however, denied charges and said he does not know any woman named Kabita.
"The allegations against me are baseless. I don't know the woman. My daughter-in-law is in my house," Mahakud told reporters.