"This incident remains under investigation by the Kansas City, Kansas Police Department's Criminal Investigations Division, who is encouraging anyone with information to call the TIPS Hotline at 816-474- TIPS (8477)", a sheriff's office statement said.
"It is very possible that with their own firearm - they were both shot", she said.
The inmate was also shot and underwent surgery on Friday. Police have not identified the suspect.
Bailiff said investigators do not believe the public is in any danger. Rohrer and King were rushed to University of Kansas Medical Center, where both died from their injuries.
Authorities say the two deputies were transporting the inmate to a hearing in downtown Kansas City when the suspect somehow got ahold of a weapon.
A spokesman for Wyandotte County, Edwin Birch, previously told CNN the shooting occurred inside the court services building, and that a juvenile had also been shot.
"We continue to pray for our brothers and sister with the Wyandotte County Sheriff's Department as we lose our sister this morning".
Charges have not yet been formally filed with the Wyandotte County District Attorney's Office.
"Let us take just one moment of silence to honor their sacrifices and the sacrifices of their families", said David Alvey, mayor of the Unified Government of Wyandotte County/Kansas City, Kan., at a press conference at City Hall. Police Officer Zac Blair says authorities are reviewing surveillance video.
The Kansas City Star reports that the shooting happened on Thursday afternoon in the north of the city.
The conditions of the deputies' are unknown.
Working major incident in the 800 block of North 7th, details unclear at this time. Zeigler said the last he heard, he was in stable condition.