A constable is a lawman. Basically, the constable was kind of a police officer and court official. The constable would arrest people accused of crimes and oversee the trial.
In chapter 15, we hear about the constable. Rachel says she heard some shouting, and asks if the “rowdy band of rivemen from a trading ship” did any damage. Matthew responds.
“Little enough, since we have a constable who is quick to his duty. The three ringleaders are cooling their heels now in his shed, and on Lecture Day they will sit for all to see in the town stocks.” (p. 164)
This is colonial justice: simple and straightforward. At least it seems this way until we learn of the witch trials. The constable’s most significant entry is when he comes to Matthew’s house to tell him that Kit has been accused of witchcraft.
“I know you don’t hold with witchraft,” the constable began, “but we’ve summat to say as may change your mind.” (p. 200)
Things get a little heated when Matthew argues with the constable. The constable is offended by what he sees as disrespect. He takes Goodwife Cruff at her word, and assumes that Kit is a witch.
“I’d trust you all right,” the constable considered. “But they’s some I don’t trust. They was out of their minds down their last night. One more death in this town and I won’t be responsible for what happens. The girl will be safe with me, I warrant.” (p. 201)
The constable is clearly uncomfortable with Kit being a girl, and he says he never figured her for a witch. He treats her fairly well, and in the end he is just doing his job.