By CBS3 Staff

SMYRNA, Del. (CBS) — Delaware State Police are investigating the homicide of a 21-year-old woman that is believed to be connected to the murder of another woman outside Smyrna Middle School on Tuesday. Troopers say they found the 21-year-old woman shot dead during a welfare check on the 800 block of McLane Gardens.

The 21-year-old woman is reportedly an acquaintance of the 38-year-old woman who was fatally shot in the parking lot of the school on the 700 block of Duck Creek Parkway on Tuesday morning. Officials say the woman arrived at the school with a 47-year-old man to pick up their daughter for a medical appointment just before 10:30 a.m.

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After a verbal argument ensued outside the vehicle, the man pulled the woman back inside the vehicle and produced a weapon and shot her. She was later pronounced dead at the scene.

As a result, the school was placed on lockdown and a search for the suspect began.

The suspect fled the scene alone in the vehicle the couple arrived in before switching to another vehicle that was registered to him and parked nearby. His vehicle was located around 11:02 a.m. in the area of Route 13 and Route 42.

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The suspect fled into Maryland and ultimately shot himself and crashed near Galenda. He was transported to an area hospital in Maryland where he was pronounced dead.

The bodies have since been turned over to the Division of Forensic Science where autopsies will be performed to determine the manner and cause of death.

Officials believe this is a murder-suicide incident and there is no concern for public safety.

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Names of the victims and suspect are being withheld pending notification of next of kin.