Although, Mohanty said he resigned on "moral grounds" after the dowry case was filed by his daughter-in-law Barsha Sony Mohanty, the State Human Rights Protection Cell has been unable to trace the minister anywhere, after he resigned 10 days ago.
The anticipatory bail was rejected by the Odisha High Court last week.
Meanwhile, the opposition party has blamed Chief Minister Naveen Patnaik as being responsible for this and has been aiding the minister by delaying his arrest.
Barsha had lodged an FIR against the minister, his wife Pritilata, his son Rajasree and other members of family. In her complaint at the Balasore police station, she alleged that she was physically and mentally abused by her in-laws for dowry a few days after her marriage in June 2012. She alleged that her in-laws demanded Rs 25 lakh and a Scorpio car from her family. She has also alleged that her in-laws and husband had tried to kidnap and kill her.
A case has been registered against the minister and others under section 498 (A), 506, 448 and 34 of IPC on the basis of the complaint lodged by Barsha, police said. In her FIR, the woman said she married Rajasree on June 24, 2012. During marriage, her parents had given Rs 10 lakh and other household articles.