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!