The suspect, Christopher Elder, 46, was in critical condition after suffering a gunshot wound, police said.
One of the victims, 37-year-old Erica Riley of Elizabethtown, had attended a court hearing in Hardin County with Elder on Monday before the shooting, police said.
The pair had been in a relationship, Elizabethtown police chief Jeremy Thompson said.
Riley's mother, 71-year-old Janet Riley of Hardinsburg, was also shot and died after being transported to a hospital, police said.
The shooting occurred in a parking lot and Elder fled the scene afterward, Thompson said.
Elder's vehicle was located on a highway by police in western Kentucky and he was pursued and stopped. Thompson said police negotiators were speaking with Elder before he turned a gun on himself.
Elizabethtown is about 72km south of Louisville.
The man who was shot was also related to Riley, Thompson said. He was in stable condition and his name had not been released.
Michael Cockerel told The Associated Press he was walking out of the Hardin County Justice Centre when he heard gunshots nearby.
He heard a series of shots and initially thought it was a nail gun from a construction site.
But after he heard a few shots, "that's when it clicked in my head that this might be gunshots," Cockerel said.
14°C