There is no specific reference to "cops" in William Faulkner's "A Rose for Miss Emily"; however, there are references to several other authorities who do have clear opinions about Miss Emily and her stubbornness. Our impression of Miss Emily as a stubborn woman is established early on when even her house is described as decaying stubbornly.
In 1894, Colonel Sartoris did what he believed to be a compassionate thing and pronounced that Emily Grierson no longer owes taxes to the town. He did this because, as a fellow Old Southerner, he did not want Miss Emily to be bothered by financial obligations once her father died. What he did, though, was create enmity in the town of Jefferson. One of its citizens (the narrator) explains it this way:
Miss Emily had been a tradition, a duty, and a care; a sort of hereditary obligation upon the town.
When the Aldermen get no response to the letter they send her to collect her taxes, they send a "deputation" to her house. The group is admitted into the house by Miss Emily's manservant, Tobe, but the meeting does not go well.
She did not ask them to sit. She just stood in the door and listened quietly until the spokesman came to a stumbling halt. Then they could hear the invisible watch ticking at the end of the gold chain.
Her voice was dry and cold. "I have no taxes in Jefferson. Colonel Sartoris explained it to me. Perhaps one of you can gain access to the city records and satisfy yourselves."
"But we have. We are the city authorities, Miss Emily. Didn't you get a notice from the sheriff, signed by him?"
"I received a paper, yes," Miss Emily said. "Perhaps he considers himself the sheriff . . . I have no taxes in Jefferson."
"But there is nothing on the books to show that, you see We must go by the--"
"See Colonel Sartoris. I have no taxes in Jefferson."
"But, Miss Emily--"
"See Colonel Sartoris." (Colonel Sartoris had been dead almost ten years.) "I have no taxes in Jefferson. Tobe!" The Negro appeared. "Show these gentlemen out."
This exchange is typical of every meeting or confrontation between the authorities and Miss Emily. They talk reasonably to her and she simply does not respond; eventually they do not even try to talk to her.
So she vanquished them, horse and foot, just as she had vanquished their fathers thirty years before about the smell.
For example, when something in her house smells, no one wants to address it with her, so they sneak over at night and put lime around the foundation. When she begins a relationship with Homer Barron, the town is scandalized and eventually sends a preacher to talk to her; he leaves the meeting completely shaken and refuses ever to go back there.
These are the kinds of things which cause the townspeople to rejoice in (or at least take great satisfaction in) any troubles that Miss Emily has and also to be intensely interested to see her house after she has died. She is intractable (unmovable) about everything in her life (including letting Homer Barron leave her), and it is a constant sense of friction and frustration with everyone in town, not just the authorities. She is a woman of the Old South and has not changed with the town; the younger people do not understand her and have very limited sympathy for her. In the end, though, it is her stubbornness which creates her conflicts with the authorities and people of Jefferson.