A Heights police officer reported seeing Petty, 46, of Morris Plains, punch the woman in the head with a closed fist near the corner of Sumner Avenue and Boulevard shortly before 1:30 a.m. Sunday, Aug. 25.
A man approached and got into a fistfight with Petty, the officer wrote in a complaint on file in Superior Court in Toms River.
The victim -- whose name was withheld -- had an undisclosed personal relationship with the schools chief, the complaint says.
Police took Petty into custody and charged him with "purposely, knowingly or recklessly causing bodily injury to another" -- basically simple assault.
Then they sent him to the Ocean County Jail.
Records show he was ordered released by a Superior Court judge later that day pending a scheduled Sept. 14 first appearance in Municipal Court in Seaside Heights.
Petty, who left as principal of a public school in Newark to become Lodi's schools chief in November 2019, has declined comment.
The topic didn't come up at Wednesday's Lodi Board of Education meeting, which was live-streamed.
Click here to follow Daily Voice Newark and receive free news updates.