Ilmi said she was trolled over her video statement on Twitter, where she had attacked the Arvind Kejriwal government over the involvement of sacked AAP minister Sandeep Kumar in a sex tape.
It also came on a day the BJP expelled Savitri Khatri, its Narela ward candidate for the upcoming municipal polls, for allegedly allowing Kumar to campaign for her.
"I left the AAP because of bad elements in it and our party (BJP) did the right thing today. Because of Kumar, Savita Khatri had to pay.
Ilmi, who had switched to the BJP from the AAP, alleged that users of the microblogging site who were "abusing" her were "AAP supporters".
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"These people follow big AAP leaders. They must be tracked through their handles and IP addresses. This is not just an insult to me, but an affront to all women. Would they use such filthy language for women in their own homes?" she asked.
When asked, Deputy Chief Minister Manish Sisodia condemned the trolling of Ilmi and promised strict action against AAP volunteers if found guilty.
"Such behaviour is unacceptable and strict action should be taken. It is wrong to troll a woman on Twitter. If AAP volunteers are found involved in this case, we will take strict action," Sisodia said.
Police confirmed receiving a complaint and said it is being looked into.