Giffords, who was shot and critically wounded in a 2011 shooting, met with U.S. Sen. Richard Blumenthal and Lt. Gov. Nancy Wyman and Newtown's first selectman, according to Sue Marcinek, an assistant to the selectman. Giffords was accompanied by her husband, astronaut Mark Kelly.
She was planning to meet later Friday with families of some of the Newtown victims, according to Steve Jensen, a spokesman for Wyman.
Giffords was left partially blind, with a paralyzed right arm and brain injury, when a gunman opened fire at a constituent meet-and-greet outside a Tucson grocery store on Jan. 8, 2011. Arizona's chief federal judge and five others were killed and 13 people, including Giffords, were injured.
The gunman, Jared Lee Loughner, pleaded guilty to 19 federal charges and was sentenced to seven consecutive life sentences, plus 140 years.
Kelly said on the day of the Newtown shooting that it should lead to better gun control.
"This time our response must consist of more than regret, sorrow, and condolence," Kelly said on his Facebook page, calling for "a meaningful discussion about our gun laws and how they can be reformed and better enforced to prevent gun violence and death in America."
Giffords' visit comes one day after Connecticut Gov. Dannel P. Malloy announced the creation of an advisory commission that will review and recommend changes to state laws and policies on issues including gun control in the wake of the Dec. 14 rampage at Sandy Hook Elementary School.
The gunman, Adam Lanza, shot and killed his mother, then drove to the school and slaughtered 20 first-graders and six educators before committing suicide as police arrived.
Giffords has appeared in public a few times since the shooting. She came face-to-face with Loughner when he was sentenced in November and attended ceremonies for the anniversary of the shooting.
She received tributes and ovations when she returned to the House in January 2012 to say goodbye as she resigned her seat and she delivered the Pledge of Allegiance at the Democratic National Convention in September.
President Barack Obama invoked the Tucson and Newtown elementary school shootings when he spoke at Newtown shortly after the attack. He said four shootings, including those two plus the attacks at a Sikh temple in Wisconsin and at a movie theater in Aurora, Colo., marked his first term in office.
A recent Pew Research Center report says gun policy accounted for almost 30 percent of discussions examined on blogs and Twitter in the three days after the school massacre. It compares the response to the Newtown rampage with the Arizona shooting, saying that in the three days after that, just 3 percent of social media conversation was about gun laws.