More than anything else, Officer Shrift seems to exist to make fun of the justice system and the law. He's basically every part of the law: judge, jury, and executioner. He can arrest Milo, sentence him, and cart him off to jail. And to top it off, there's nobody else there to stop him or provide balance to the legal system. (In case you're unfamiliar, this is definitely not how it works in the real world).
Like almost everything else in The Phantom Tollbooth, Officer Shrift's name is a pun:
[He was] the shortest policeman Milo had ever seen. He was scarcely two feet tall and almost twice as wide, and he wore a blue uniform with white belt and gloves, a peaked cap, and a very fierce expression. He continued blowing the whistle until his face was beet red, stopping only long enough to shout, "You're guilty, you're guilty," at everyone he passed (5.6).
So, he's short, and his name is Shrift. So what? Well, have you ever heard the expression "short shrift"? It means "to give little consideration to" something (source), which is precisely what the officer does: he just decides that everybody's "guilty" as soon as he sees them.
Officer Shrift's examination of Milo is brief, and he keeps cutting off our protagonist so that he can make up a new crime of which the boy can be guilty. For example, he blames Milo for not knowing his (the officer's) birthday: how on earth would he know that? But we have to cut our officer friend some slack. After all, Rhyme and Reason are gone from Wisdom, so how can we expect him to be reasonable?