The Bihar police case was registered under various IPC sections including 341 (wrongful restraint), 342 (wrongful confinement), 380 (theft in dwelling house), 406 (criminal breach of trust), 420 (cheating) and 306 (abetment of suicide).
Singh accused Chakraborty, a budding TV and film actress, of having befriended his son in May, 2019 with the intention of furthering her own career.
The ED's interest, they said, is into the allegations of alleged mishandling of Rajput's money and his bank accounts.
The agency will probe if anyone used Rajput's income for money laundering and creating illegal assets, they said.
The ED can attach assets of the accused and also has the power to make arrests under the PMLA.
The Mumbai police is already probing Rajput's death.
Rajput (34), who had starred in films such as 'Chichhore', 'Kai Po Che' and 'Kedarnath', was found hanging in his apartment in Mumbai's Bandra area on June 14.