Dikshit refused to divulge details of her meeting with Shinde but said law and order situation in the city as well as the alleged suicide of Singh figured in the talks.
"A magisterial inquiry has already been ordered. Till the report comes, it will be difficult to comment on the issue. Let the autopsy report come, things will be clear," Dikshit said.
Though Tihar authorities said Singh was found hanging, his family and lawyers claimed it was a murder.
Sources said Dikshit in the meeting with Shinde raised the issue of security inside the Tihar prison. Tihar officials said the magisterial inquiry will also probe any possible security lapses inside the high-security jail.
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The Delhi Chief Minister said she did not come to meet Shinde because of alleged suicide of Singh. "It was a routine meeting. I keep coming here. The meeting was prescheduled," she said.
Sources said Dikshit also took up the issue of policing in the capital and asked Shinde to take "specific steps" in ensuring better security for women. The Delhi Police functions under direct control of Home Ministry.
The Chief Minister is understood to have expressed concern over no let up in crime against women despite Centre's assuarnce in the wake of the December 16 gangrape incident that all measures will be taken to ensure safety of the fairer sex in the city.