"The inquiry report is delayed because statements of some people concerned are yet to be recorded," DCP, Zone 10, Vinayak Deshmukh told PTI.
The incident involving the duo, who work at a call centre in suburban Malad, took place on the night of November 1 and its clipping soon went viral on social media, evoking strong reactions from various quarters.
The state government had asked Deshmukh to conduct inquiry to determine if police had used force in violation of rules.
According to them, the duo were brought to the police station since they were under heavy influence of alcohol and fighting with each other on road near Andheri Metro Station.
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The video of the incident was shot by police informer Maqbul Sheikh who was present inside the police station to give some information, Deshmukh said.
"Sheikh had submitted an application to the police complaining about the police officers allegedly beating the couple," he said.