The plaintiffs include a survivor and relatives of nine people killed in the massacre.
A Washington Post database says there have been 162 mass shootings in the United States since 1966, but numerous deadliest incidents have occurred in the past few years.
Bushmaster is owned by Remington.
"Today's decision is a critical step toward achieving that goal", he added.
It also concluded that CUPTA lawsuits are not barred by a federal law that generally protects gun suppliers from civil liability for crimes committed with their products.
Four days after 20 children and six adults were killed at Sandy Hook Elementary School, most students in Newtown returned to school.
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The lawsuit, which was filed in 2015, was dismissed in 2016 by a lower court, ruling that gunmakers have broad immunity from liability under a federal law known as PLCAA, the Protection of Lawful Commerce in Arms Act.
Long-frustrated efforts by the families of kids killed by gun violence to hold manufacturers responsible for their deadly wares struck at least temporary pay dirt in a Connecticut Supreme Court decision today.
The suit claims the company marketed and promoted the gun for civilians to use to carry out "offensive, military combat missions against their perceived enemies", and CT law bars ads that promote or encourage violent behaviour, the court said in its 71-page ruling.
Joshua Koskoff, a lawyer for the plaintiffs, has said the Bushmaster rifle and other AR-15-style rifles were designed as military killing machines and should never have been sold to the public. An eventual ruling against Remington could establish legal precedent, opening doors for more lawsuits against gun manufacturers, and expose the company's communications about its marketing plans.
The lawsuit was originally filed in 2015 by nine families and a teacher who was injured in the attack and also names as defendants distributor Camfour Holding and Riverview Gun Sales, where Lanza's mother Nancy purchased the gun as a gift for her son's 18th birthday. The plaintiffs argued that supplying military-style rifles to civilians in itself qualifies as negligent entrustment, a cause of action that involves transferring a "dangerous instrumentality" to someone whom the defendant knows or should know is apt to cause harm with it.
The decision represents a major victory for the families of the 20 first-grade children and six educators who were killed in one of the deadliest mass shootings in USA history, which inflamed outrage among gun control advocates who demanded lawmakers work to prevent mass shooting. Several groups, ranging from the National Rifle Association to emergency room doctors, submitted briefs to the court.
Still, allowing the lawsuit to move forward means that there will be an opportunity for discovery that would unearth company documents that could be embarrassing for Remington.