Opposition leader Ajay Singh said they have submitted a letter to state chief secretary in this regard.
The incident occurred on December 15 evening when the constable Ratnesh Pawar allegedly pointed his service rifle at the senior Congress MP who was about to board a private plane for Delhi from the airstrip.
However, alert security guards of the Congress leader overpowered Pawar.
"I have submitted a letter to state chief secretary requesting him to order an inquiry by a special investigation team (SIT) into the incident in which a state police constable pointed his gun at Kamal Nath," Leader of Opposition Ajay Singh said.
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"If the police constable was mentally sick, then why was he deployed in the former union minister's security?" he asked.
Singh claimed that some RSS literature was found at the residence of Pawar in Chhindwara.
However, Chhindwara DIG G K Pathak denied recovery of any such material.
"No literature of any outfit was found at Pawar's residence. We are conducting a thorough inquiry into the matter. It is up to the state government to take a decision on an SIT investigation," Pathak said.
"The police constable was booked under IPC sections 308 (Attempt to commit culpable homicide)," the DIG said.
He said though the constable was undergoing treatment for his mental illness he did not disclose it to police department as he feared losing his job.
"The documents related to his illness were found at his residence," Pathak said.
The officer said Pawar, suspended after the incident, was admitted in the psychiatric unit of Subash Chandra Bose medical college in Jabalpur for a detailed examination of his mental status.