Yes, there are laws that govern Waknuk society; however, often readers are meant to infer what the general wording of a law is because there are few locations in the text where a law is quoted in a word-for-word format. We get close in the early parts of the book when David is telling us about "ethics."
Ethics was why you should, and shouldn't, do things. Most of the don'ts were the same as my father's, but some of the reasons were different, so it was confusing.
David tells readers that ethics covers why certain things should be done and not done. It covers why rules are in place, but it doesn't necessarily explain what those rules are. A few paragraphs later, David tells readers that there are a lot of rules that govern his society and ethics. Thankfully, instead of listing all of them, he summarizes the rules in a couple of sentences.
Most of the numerous precepts, arguments, and examples in Ethics were condensed for us into this: the duty and purpose of man in this world is to fight unceasingly against the evils that Tribulation loosed upon it. Above all, he must see that the human form is kept true to the divine pattern in order that one day it may be permitted to regain the high place in which, as the image of God, it was set.
Ultimately, the most important and overarching rule of the entire society is the rule to preserve the image of the human form. The rules about the ideal human form are taught to children in the commandments and precepts, and kids are made to memorize those rules. For example, there is this quote that clearly describes what a person should look like.
And God decreed that man should have one body, one head, two arms and two legs: that each arm should be jointed in two places and end in one hand: that each hand should have four fingers and one thumb: that each finger should bear a flat finger-nail. . . .
Anybody that doesn't fit those characteristics is labelled "Deviant," and one of three things happens to them by law. They are executed, expelled to the Fringes, or sterilized. In each case, the end result is the same. Their deviant genetic code is removed from the Waknuk gene pool.