There are teams that normally have different captains for different cricket formats but it is not a common practice in the Indian cricket board. India is already playing well under Kohli's captaincy right then why there is a need for a change now? At least it is better to give time until the next WorldCup for Kohli to prove his captaincy skills before criticizing and talking about changing capitans.
The main accusation against Kohli is that he does not take any tactical decisions if things are not going your way, the team wins because of his aggressive approach and the way in which he leads the team from the front scoring runs and on their day they will defeat any team in the world and the upcoming world cup will be a big test for Kohli as a captain in T20 internationals.