When Rajiv got assassinated Congress was with AIADMK. And as you said Karunanidhi was the CM. But Rajiv was not a PM at that time.
Now I can ask where the Jayalalitha went when Rajiv was campaigning for her. OK leave Jayalalitha. Where the other Big shots of Congress went. Where Mr.Moopnar / Mr.Valapaddi went(Even thought it is not our manner to talk about someone who is not with us anymore , I am noting there name to explain the history).
Just like that don't blame TN Govt. Just see the Elam Issue with open eyes. Better read there history.