In a statement on Thursday, Arnold Randall, the general superintendent of the Forest Preserve District, said officials had apologized directly to the woman involved, Mia Irizarry, and had refunded the money she paid for a permit. Mr. Randall also said he hoped Ms. Irizarry, 24, would consider returning to the park.

“I am sincerely sorry this happened,” he said. “I’ve seen the video, and I am outraged that this would happen anywhere, but especially sad it happened in our Forest Preserves.”

Some aspects of their investigation are continuing, he said, noting that Officer Connor’s personnel file would reflect that he “did not resign in good standing.”

Repeated attempts to reach Mr. Trybus and Officer Connor for comment have been unsuccessful.

The episode took place last month in the northern Chicago park Caldwell Woods. The recording, taken by Ms. Irizarry, shows Mr. Trybus demanding to know why she has a Puerto Rican flag shirt on and whether she is a United States citizen. While Mr. Trybus shouts at Ms. Irizarry, points at her face and follows her around part of the park, Officer Connor can be seen standing about 20 feet away with his hands against his chest.