Authorities were expected to release the names of the victims Tuesday.
Two police officers were also shot, but were treated at a hospital and released. Chief William Jopp of the Capitol Police, which provides security at state government buildings, said they were protected by their bulletproof vests.
Authorities said the gunman opened fire in the lobby of the courthouse, where people line up to go through metal detectors.
“He did not break the (security) perimeter,” Shavack said.
Jose Beltran, 53, an employee at the courthouse, said he heard two shots, “Boom, Boom,” as he was entering the lobby. Beltran said he heard at least three more shots as he turned around and ran.
“It happened so fast,” he said.
After the shooting, police searched the courthouse room by room as a precaution. Streets around the courthouse remained cordoned off Monday night.
Diana Dorn, who lives right behind the courthouse, said she heard the shooting from her bedroom window.
“You could hear it really clear,” she said.
In response to the shooting, Delaware Gov. Jack Markell’s office said he would return early from a trade mission to India.
“While this shooting is notable for the fact that it took place inside a state courthouse, there are some aspects of this incident that are, unfortunately, all too common,” Markell said in a statement. “I am saddened that two more brave members of our law enforcement community have been injured in the line of duty. I am also saddened that this appears to be another example of a domestic situation that turned deadly.”