Yelburton plays it cool—as cool as you can be when your name contains the word "yell"—but he's covering up a crime against the public.
He's the deputy chief of the water department who's in cahoots with Noah Cross, supporting his plan to steal the city's water supply. At one point, Jake tells Yelburton that he thinks he's involved with Hollis Mulwray's murder, and that he's seen the water department secretly draining water from the reservoirs.
Yelburton acts all calm and collected, responding:
YELBURTON: We're... well, we're not anxious for this to get around, but we have been diverting a little water to irrigate orange groves in the northwest valley. As you know, the farmers there have no legal right to our water, and since the drought we've had to cut them off—the city comes first, naturally. But, well, we've been trying to help some of them out, keep them from going under. Naturally when you divert water—you get a little runoff.
This is a total lie, and Jake ain't buying it. But it's the same story Yelburton and Cross use to fool the cops later in the movie, discrediting Jake and making sure that they succeed in their dastardly designs.
So, behind this mild-mannered bureaucrat, there's a Grade-A shyster. He and Noah could've taught Bernie Madoff a thing or two.