Rohrer and King had pulled up into the courthouse's back parking lot shortly after 11 a.m. Friday and were taking the suspect out of an inmate transport van when they were attacked, Wyandotte County Sheriff's Office spokeswoman Kelli Bailiff told reporters at a news conference.
The suspect, who has not been officially identified, was also shot multiple times and was taken to the hospital, where he was said to be in stable condition.
Both deputies were taken to the University of Kansas Health System, where one of the deputies succumbed to his injures, said Kansas City police Chief Terry Zeigler. Patrick Rohrer, 35, died first and Theresa King died at 12:20 a.m. Saturday, the sheriff's office said.
Rohrer had been with the department for seven years and King for 13 years. Kelli Bailiff said. King, 44, died early on Saturday at a hospital.
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King had three children, Bailiff said, and Rohrer had two.
Zeigler said the authorities were withholding the inmate's name until he's been formally charged, which is expected to happen next week. Video from the scene shows the courthouse surrounded by yellow police tape, several police vehicles parked in the street and numerous uniformed law enforcement officers walking the grounds.
Bailiff said the inmate was being taken across the street from the jail, to the services building, for a court hearing.
Lyon County Undersheriff John Koelsch says inmate transfer situations carry an inherent danger. No other details were released about the suspect, including his condition.
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Kansas City police spokesman Zac Blair said officers were speaking to witnesses about shooting.
The Olathe Police Department, Raymore Police Department in Missouri and the Jackson County Sheriff's Officer in Missouri tweeted similar heartfelt messages.
"We're saddened to hear the tragic news out of Kansas City today".
Kansas Gov. Jeff Colyer (R) was told of the shooting on Friday as he arrived for a forum in Kansas City.
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In 2015, Wyandotte County Deputy Scott Wood was shot seven times but survived. Kansas City Police Capt. Robert Melton, 46, was gunned down while chasing suspects of a drive-by shooting on July 19, 2016.