Kant alleged that some police personnel in civil uniforms made an unsuccessful attempt to abduct him when he came out of his residence in Sector 18 of the city.
He said he immediately called Police Control Room (PCR), after which personnel from Chandigarh police rushed to the spot and rounded up at least five persons.
Kant said he was to go to Fatehgarh Sahib district in Punjab today to join Aam Aadmi Party (AAP), but he had postponed his plans for some time.
Meanwhile, Chandigarh police said it was investigating the matter and verifying the credentials of some persons who had been rounded up outside Kant's residence.
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The former DGP alleged that the Punjab government was "patronising" drug peddlers in the state.
Earlier, Kant had alleged that politicians from major political players, including Akali Dal and Congress, in the state and certain senior policemen were "patronising" drug mafia in Punjab.
He had said a 'Peoples Commission' comprising former or retired judges, advocates and other prominent persons had been set up to fight the drug menace in Punjab.
He had said two key issues confronting the state were drug sale and human rights violations.
The issue of drugs in Punjab was highlighted after alleged drug smuggler Jagdish Singh Bhola had accused Revenue Minister Bikram Singh Majithia of being "directly involved" in drug racket, following which opposition Congress had sought CBI probe into the matter even as the Minister denied the charges.