Wishing Thackeray on his birthday, the former Delhi BJP president pointed out that 43 days had passed since Rajput died, but no FIR was registered so far.
"Many happy returns of the Day @CMOMaharashtra Shri Uddhav Ji, on this day I request with folded hands to give justice to Sushant who died 43 days ago, but no FIR has been registered so far," Tiwari tweeted.
"I hope you will help. Please do justice to millions of SSR fans," he tweeted.
The Bhojpuri singer and actor, who represents Northeast Delhi Lok Sabha seat, said when he visited Rajput''s family in Patna last month, "his father and sister requested me to take up the issue and get Sushant justice. It was really a sentimental moment for me".
Earlier, Tiwari had demanded a CBI investigation into death of the actor, who was found hanging at his apartment in suburban Bandra on June 14.
"To my surprise, even 43 days after Sushant''s death, no FIR is registered in Mumbai. So the case cannot be transferred to the CBI," Tiwari told PTI.
Mumbai Police should register an FIR immediately so that proper and impartial investigation could take place, he added.
In its ongoing investigation in the case, Mumbai Police have recorded statements of nearly 40 people.