Remaining decorative concrete slabs on Centennial Hall will be removed after one of them fell off on Friday.
Deputy County Administrator Monnie Gore said work is expected to begin as soon as this week.
Monday morning, structural engineers inspected the panels.
The concrete block that fell was 3 feet wide, 10 feet long, 6 inches thick and weighs more than 2,000 pounds. It broke into many pieces.
El Paso County Commissioners said the slab is more than 30 years old and they believe the steel that held it up was corroded.
Centennial Hall is owned by El Paso County and was built in 1976.
The complex is home to several county offices, including the Board of County Commissioners. The area where the slab fell is home to the El Paso County Clerk and Recorders office.