The complaint has been filed by sub-inspector Ashok Avchare, of the Ambad police station in Maharashtra's Jalna district.
Mr Avchare was heading the investigation into the disappearance of one Bhausaheb Kisan Rathod, who went missing on June 7. A missing complaint was lodged with the Ambad police station.
During the investigation, Mr Avchare came to know that Mr Rathod had borrowed Rs 3 lakh from an agent of a sugar factory and was not repaying the amount, police said.
Later, the agent reportedly asked Suresh Chavan, a support of Mr Kuche, to recover the money from Mr Rathod. Mr Chavan had been allegedly harassing Mr Rathod over the pending amount, they said.
Mr Avachare called Mr Chavan for inquiry and told him he will register a complaint against him in connection with the disappearance of Mr Rathod, police said.
Mr Chavan reportedly called Mr Kuche and told him about the likely police action. Mr Kuche then called Mr Avachare and allegedly threatened and abused him for trying to "implicate" Mr Chavan in the case, they said.
Mr Avachare also made an entry in the police dairy regarding the incident. He yesterday submitted a written complaint against the MLA from Badnapur constituency in the district to in-charge of the Ambad police station.
Additional Superintendent of Police Lata Phad confirmed the filing of complaint against the legislator.
Ms Phad did not provide further details, saying she was still looking into the matter. Mr Kuche was not available for comment.