Heriot said the shooter then exchanged gunfire with police before falling.
Delaware State Police Sgt. Paul Shavack said the gunman and the women are dead. Mayor Dennis Williams said in a phone interview that one of the women killed was the shooter's estranged wife, but Shavack said police had not confirmed that.
Shavack also declined Monday night to confirm Heriot's account of the shooting, or disclose who shot whom, saying investigators were still reviewing surveillance video and taking witness statements.
Authorities said Monday evening that autopsies had been completed on the two female victims, but they were withholding their names while family members were notified. However, 6ABC identified the intended target as Christine Belford.
Delaware Attorney General Beau Biden said at a news conference that the shooting was not a random act of violence.
"It's developed out of a long - over the course of many years - custody dispute in the courts of this state," Biden said.
Authorities said 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 armored vests.
Authorities said the gunman opened fire in courthouse lobby, where people line up to go through metal detectors.
"He did not break the [security] perimeter," Shavack said.
After the shooting, police searched the courthouse room by room as a precaution. Streets around the courthouse remained cordoned off Monday night. Officials said the courthouse would remain closed Tuesday while repairs were made and authorities continued their investigation.