Rajput's brother-in-law O.P. Singh, who is the Additional Director General of Police and posted as Special Officer in the Haryana Chief Minister's Office, suspected some foul play in the crime, it is reliably learnt on Monday.
He is now seeking a thorough probe into the incident.
State officials said Singh has left for Mumbai soon he came to know about the suicide incident.
Expressing condolences, Haryana Chief Minister Manohar Lal Khattar said actor Rajput's death is an "irreparable loss" to not only the film industry but also for the entire society.
Meanwhile, Bollywood continued expressing grief and disbelief over the demise of Sushant Singh Rajput, all of Sunday. The 34-year-old actor was found hanging in his residence by his maid on Sunday morning.