Police pumped tear gas into the home in an attempt to get the gunman to leave, and then went into the home and shot him, ABC News Denver affiliate KMGH-TV reported.
The three people found dead in the home are believed to be relatives of the shooter, Aurora Police Sgt. Cassidee Carlson told KMGH. A fourth person was found unharmed, she said.
Officers responded to the home after the first reports of gunshots came in around 3 a.m.
"We're just getting in there with our crime scene detectives, so obviously we'll have to determine if it was our rounds or his rounds," Carlson said. "This is a big investigation, and a lot is entailed."
Carlson said neighboring residences were evacuated while the SWAT team attempted to resolve the standoff.
"We've evacuated several residences in the neighboring townhomes and in the immediate area where we believed would be the most dangerous," Carlson told KMGH-TV earlier today.
The Colorado town was the site of a movie theater massacre last July. A gunman opened fire during a midnight screening of "The Dark Knight Rises," killing 12 people and injuring 58 others.