At the initial murder scene there is a stream of blood that comes out of the head injury to Sam. But when Vijay returns to check the the spot the blood has vanished and floor is clean and concludes that there must have been internal bleeding.
Despite having no proof, no evidence and no witnesses supporting her, IGP Meera Deshmukh was able to reconstruct Vijay's plan perfectly as if she was there and saw the whole thing happen. It would have been practically impossible for her to figure any of those details out with the information she had.
IGP Meera Deshmukh says that she can't put Vijay's family on a lie detector test without a court order, yet she has no problem torturing them to force a confession. It makes no sense for her to seek court approval for one thing and then just break the law anyways.