Padukone was among six people - including two other actresses - to be summoned for questioning over the case.
Rajput's girlfriend, Rhea Chakraborty, was arrested earlier this month for allegedly buying drugs for him - claims she has denied.
The case has fuelled months of media coverage and speculation in India.
The Narcotics Control Bureau (NCB) widened its investigation of the case on Saturday, questioning Padukone for six hours in Mumbai.
