Leavitt said a patrol officer arrived at the school and ordered Killough down from the fence. She complied and was taken into custody without incident.
The spokesman said that Killough seemed impaired at the time.
KVVU-TV in Las Vegas interviewed some of the students who said they witnessed Killough's alleged climb.
"It was so scary," Gael Duarte, a fourth-grader, told the news station. "I heard a lady screaming, 'I'm going to kill you.' I saw a lady screaming at all of us with an ax beside her."
Fourth-grader Naomi Ramirez said she had tears in her eyes when she saw what happened.
“I was shaking,” Naomi said. “My friends tried to calm me down, but I couldn’t do it.”
KVVU obtained a letter that Kristie Cole, principal of the elementary school, sent to parents to inform them about the incident.
"We want to let you know that earlier today, an adult not associated with our school attempted to climb a fence to trespass on campus," Cole wrote. "Staff and students noticed the woman and law enforcement was called."
The letter assures parents that Killough was taken into custody before she could access the playground and that no one was injured. Cole thanked the police officers for their prompt response time, as well as the students and staff who were alert and took action.
"This incident serves as an important opportunity to remind our parents and students of safe practices, and to look out for each other," Cole wrote.
School safety has been a hot-button issue throughout the country since the Valentine's Day mass shooting at Marjory Stoneman Douglas High School in Parkland, Florida, that killed 14 students and three staff members. Nikolas Cruz, a former student who had been expelled, has been charged with 17 counts of murder.