Smyrna resident Stephanie Gill, 38, was shot in the parking lot of Smyrna Middle School around 10:25 a.m. Tuesday.
According to investigators, the victim and the suspect, 47-year-old Llewellyn Gill of Hartly, arrived at the school together in Stephanie's vehicle to pick up their daughter for a medical appointment.
Police said the couple argued outside of the car before Llewellyn Gill pulled Stephanie Gill into the vehicle and shot her. She was pronounced dead at the scene.
The school was placed on lockdown while authorities searched for the suspect. No students or staff were injured.
According to police, Llewellyn Gill left the school parking lot in the vehicle but ended up switching into another vehicle that was registered to him and parked nearby.
Troopers located that vehicle at about 11 a.m. near Route 13 and Route 42 and a pursuit began. The suspect led police into Maryland and ultimately shot himself and crashed near Galena, Md., authorities said.
The suspect was taken to an area hospital where he was pronounced dead.
During the investigation, troopers learned of a second victim who was an acquaintance of Stephanie Gill.
Officers then responded to the 800 block of Monrovia Avenue in the McLane Gardens Apartments in Smyrna to check on the welfare of 21-year-old Deanna Dominick-Dalton of Clayton.
Police found her inside the home with apparent gunshot wounds. She was pronounced dead at the scene.
Neighbors said they don't know why Dominick-Dalton was at the couple's home on Tuesday.
They noted that the victim's husband had been living elsewhere while the couple worked out some issues.
Neighbors said the couple does leave behind several children.
Anyone with information regarding this incident is asked to contact Sergeant Yeich at 302-741-2703 or Delaware Crime Stoppers at 1-800-TIP-3333.