"Given how wide the net would have to be cast and given the problem of false positives in testing it is much more likely we would go ahead and find some misleading genetic markers, which would later be proven false while unnecessarily stigmatizing a very large group of people," Bursztajn said.
Bursztajn also cautions there are other risks to this kind of study: that other warning signs could be ignored.
"It's too risky from the stand point of unduly stigmatizing people, but also from distracting us from real red flags to prevent violence from occurring," Bursztajn said. "The last thing we need when people are in the midst of grief is offering people quick fixes which may help our anxiety, but can be counterproductive to our long term safety and ethics."
Bursztajn is also the president of the American Unit of the United Nations Educational, Scientific and Cultural Organization (UNESCO) Bioethics Chair and in that role he teaches health care professionals about responsible genetic education including the history of eugenics in this country in the 1920s and Nazi Germany. He cautions against the slippery slope that the kind of research that could be involved in the University of Connecticut's study could lead to.
Dr. Heidi Tissenbaum, a geneticist at the University of Massachusetts medical school, agrees the research is risky saying an accurate study just cannot be completed on one person.
"The problem is there might be a genetic component, but we don't have enough of a sample size," Tissenbaum said. "I think it's much more than a simple genetic answer, but an interplay between genetics and environment."
"One sample, what's that going to tell you," Tissenbaum said, referring to Lanza's DNA. "You never do an experiment with one, you can't conclude anything… The question is what are they comparing his DNA against? Are they going to control to random people? Matching for age or society? We just don't have enough (of a sample)."
Tissenbaum says the rush to study his DNA may simply be because "people are hurting so much they would like to find a quick answer."
"Even identical twins are different and they have identical DNA," Tissenbaum noted.
ABC News' Dr. Amish Patel contributed to this story.