Hal Slocumb is seriously the only sympathetic male character in the film. And by sympathetic, we don't mean he sympathizes with Thelma and Louise (though he does); we mean he's the only real nice guy in the film's world of total male one-dimensional jerks.
We first encounter our friendly detective talking to a server from the roadside bar Thelma and Louise fatefully stopped at along their journey, after Thelma's would-be rapist's body has been discovered. He sees the murder for what it is: messy. And we don't just mean blood-and-guts-wise: something doesn't add up, and Hal knows it.
In a world where sexual assault cases seem to end up protecting the assaulter more often than the victim, Hal is a godsend. However, his powerlessness—don't forget that image of him scurrying after Thelma and Louise's car as they drive it over the cliff—is a big deal in the narrative of the movie. He wants a fair trial for Louise, in particular, but he's stuck in a system that won't relent. He tells Louise he knows what happened to her in Texas. In other words, he totally gets why she shot that guy. But will the justice system see that as legit?