The 30-year-old man produced an identity card of a doctor engaged with a healthcare establishment in Pune but it turned out to be fake.
A senior Kolkata Police officer said the man wanted to meet the chief minister yesterday on the pretext of expanding the healthcare facility in the state.
Ms Banerjee was away in north Bengal yesterday.
Several documents have been seized from the man, identified as S K Aynal of Bankura district of West Bengal.
"He failed to clarify why he needed to visit the CM's residence. His answers are unsatisfactory. We are questioning him to get more details," he said.