By Dan Koob

SMYRNA, Del. (CBS) — Some frightening moments at a Delaware middle school Tuesday. Students were forced into lockdown after a woman was shot and killed just feet away in the school’s parking lot.

No students were injured as the gunfire erupted at Smyrna Middle School.

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There are a lot of unanswered questions as this investigation continues. One of the biggest questions is, why did the shooting happen in front of this school when neither of those involved are school employees?

“A traffic stop was initiated, but the suspect fled,” Smyrna Police Corp. Jason Hatchell said.

An interstate chase ended on the side of a Maryland road, Smyrna police say, after a 47-year-old Smyrna man shot and killed a 38-year-old woman in front of the town’s middle school Tuesday morning.

“They are family, but we’re still working on ironing out exactly what their relationship is,” Smyrna Police Lt. Brian Donner said.

Officials say an argument led to the shooting in the school’s parking lot, but the woman is not an employee.

A school resource officer quickly responded, but the woman was pronounced dead.

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Superintendent Patrick Williams says all district schools were then locked down.

“That occurred within minutes after the actual incident. We then alerted our community, our families and our staff to let them know that all of our schools were in a lockdown protocol. And we confirmed that all staff and students were safe,” Williams said.

“I don’t know what this place is coming to, but it’s scary,” said Stacia Kain, the mother of a teacher at the school.

Children were escorted by staff to the adjacent high school once the lockdown was lifted.

Police are still investigating why the woman and the 47-year-old suspect ended up in front of the school.

“It’s tough, the whole community is gonna be shook. There’s no doubt about it. This is a small, close, tight-knit community. A lot of the community-type events are organized through the school district so it hits extra close to home because of that. People will be shook for a while, there’s no doubt about that, and this is not common to have this happen every day,” Donner said.

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Smyrna police say this is the first homicide to take place in this Delaware town in nearly two years.