Siblings Henry Carter Jr., 5, and Alexis Carter, 3, died in the Aug. 15 fire at the Colonial Gardens Apartment Complex in the 8800 block of Broadmoor Court.
The suit was filed in Johnson County District Court by their parents, Henry Carter and Allysa Carter-Mondoza.
It alleges that smoke detectors in their apartment were not properly installed and carbon monoxide detectors were not working at the time of the fire.
The family moved into the apartment in June 2016, according to the suit.
The suit alleges that the management of the apartment complex was negligent in failing to provide "proper maintenance and inspections" that would have discovered the conditions of the smoke and carbon monoxide detectors.
The management company failed to train its employees to properly install smoke detectors and failed to warn the family that the carbon monoxide detectors were improperly installed, according to the suit.
Henry Carter, their father, also suffered severe burns when he tried to rescue the children, according to the suit.
The person who answered the phone at the apartment complex office on Monday said they had no comment about the suit.