In her complaint, the woman alleged that Kumar had offered her a spiked drink in his office in outer Delhi's Sultanpuri where she had gone to seek his help in procuring a ration card. The woman has alleged that after she fell unconscious, he raped her.
Earlier in the day, AAP's Political Affairs Committee suspended the 36-year-old first-time MLA from the party and refered the matter to its disciplinary committee.
The MLA from Sultanpur Majra surrendered before the investigators at the office of DCP (Outer) in Pitampura where his statement was recorded, senior police officials said.
In her complaint filed at Sultanpuri police station, the woman claimed the CD was made after Kumar became minister and that she did not know about it.
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Her statement is being recorded, Sanjay Singh, joint commissioner of police (Northern range) said.
Delhi chief minister Arvind Kejriwal tweeted that if the allegations were found to be true, then Kumar should be given "exemplary punishment".
"If woman's allegations are correct, this is v serious. Strongest exemplary punishment shud be given to Sandeep," Kejriwal who is in Rome to attend Mother Teresa's canonisation tweeted.
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