The apex court asked whether constitutional authorities can act illegally, according to reports.
The SC also slammed Delhi Police for inaction and questioned the force over the unlawful assembly of people which gathered despite prohibitory orders under section 144 CrPC in force.
The court also wanted to know whether police acted appropriately to get the assembled people dispersed.
The police have been asked to file a reply by January 31.
The notice came in response to a public interest litigation (PIL), filed by advocate ML Sharma, which had questioned whether a person holding a constitutional authority can sit on a dharna.
The PIL was filed on the agitation by Kejriwal in the heart of Delhi calling for the suspension of five policemen who the Delhi government said had failed to act on the orders of Bharti.
Bharti has also been made a respondent in the PIL which stated that the law minister, who triggered the controversy, took the law in his own hands and so action must be taken against him.