Safety issues such as lack of inspections and the use of substandard materials have plagued construction projects in the country.
The accident took place in an area near Girish Park, one of Kolkata's most densely populated neighbourhoods, with narrow lanes, and shops and houses built close together.
The 2km-long (1.2 mile) flyover has been under construction since 2009 and missed several deadlines for completion.
The causes of the disaster were not immediately clear, but the company in charge of the construction, IVRCL, said it would cooperate with investigators.
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Source: BBC