Why does Katniss decide to have as little as possible to do with Peeta in The Hunger Games?
I am going to assume that you are referring to Katniss and Peeta as they are presented in The Hunger Games and not in either of the other two subsequent novels, Catching Fire and Mockingjay.
In The Hunger Games, Katniss and Peeta are both tributes from District 12 and are have known each other for several years, but in terms of the games, there can only be one winner, and so it would be dangerous to trust anyone too much. Katniss is unsure what to make of Peeta's behavior, so she is cautious in her interactions with him. Much as she may like to have a friend in the arena, there are no friends in a fight to the death.
Some of Peeta's behavior is upsetting and disconcerting to Katniss. He is friendly while in the training center, but then he turns very cool towards her. She doesn't know what to make of that. Then, he announces to the televised audience that he has always had a crush on Katniss. She is shocked by this revelation and soon finds out that Haymitch and Peeta have planned this all for the sake of their television personas in the hopes that it will make them popular and garner them fan support and gifts. Katniss sees the positive in this, but doesn't know if she can trust it. Once they are in the games, Peeta joins in with an agressive group of careers and Katniss is confused about where Peeta's loyalties lie. She starts to question what is part of the act and what isn't. This doubt is plays a part in her decision to play things cool with Peeta. It is only after she realizes that trusts Peeta more (like after the trackjacker attack) and after she receives rewards for her "relationship" with Peeta that she lets him in a little closer.
Ultimately, their closeness and their trust in each other saves them both from the games -- a first for the annual event!
Katniss already felt indebted to Peeta because he had once saved her family by giving her bread when her family was starving. Both of them were now players in the Hunger Games and their objective was to eliminate the other players. If she began to know him better and develop an emotional attachment to him, it would be harder to kill him as the act would invoke feelings of guilt.
I am going to tell you about Katniss's perspective before she entered in the arena with him.
She decides to do as little as possible with Peeta because she assumed in the beginning that she had to kill him. and killing him would be much easier if she didn't know about him. Thus, because she had in her mind that peeta might be killed in the arena it will be easier if she was not the one to do the same or if she didn't know him that well...
hope this answer helped you.