The Delhi assembly has been in suspended animation since Feb 2014 after Kejriwal quit as chief minister.
"Media reports suggest that the Lt. Governor of Delhi has recently sent a report to you recommending that the single largest party i.e. BJP be invited to form government. Such a recommendation would be an open invitation for the formation of government by defections and horse trading," reads the letter submitted by AAP to the President.
Delhi Lt. Governor Najeeb Jung Friday had sought President Pranab Mukherjee's permission to invite the single largest party in the state assembly - the BJP - to form the government in Delhi.
Reacting to the Bharatiya Janata's Party's statement that there was a provision in the law that offered legislators the option to choose the chief minister through a secret ballot, Kejriwal claimed it was not possible.
"The counting of secret ballot is not possible. I have met several constitutional experts on the matter who have confirmed that that is completely against the constitution," he told media after his meeting with the President.
The BJP had won 31 seats in the 70-member house but now has 28 legislators after three were elected to the Lok Sabha in the general elections held April-May.
In a house with an effective strength of 67, the lone Akali Dal legislator is a BJP ally. There is a JD-U member, an Independent and an AAP rebel.
The Congress won eight seats.