According to the Des Moines Register, the first and second floors of the Wallace Building in downtown Des Moines tested positive for the potentially dangerous dust.
About 495 state employees work in the building.
The tests were run by the Department of Natural Resources.
If inhaled or ingested lead can cause damage to a person’s nervous system, kidneys, blood forming organs and reproductive systems.
State officials say the employees’ health is not in immediate danger though.