(CNN) One sheriff's deputy is dead and another is in critical condition after they were shot Friday during a prisoner transport in Kansas City, Kansas, authorities said.

The two Wyandotte County deputies were transporting inmates to court around 11:30 a.m. CT Friday, sheriff's office spokeswoman Maj. Kelli Bailiff said at a news conference.

When they pulled into a parking lot outside the county courthouse, the deputies were "overcome," Bailiff said.

"It is very possible that with their own firearm -- they were both shot," she said.

Deputy Patrick Rohrer was fatally shot by an inmate during transport, authorities said.

Police identified the slain deputy as Patrick Rohrer, 35, a seven-year veteran.

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