In the aftermath of the rampage at Sandy Hook Elementary School in Newtown, where 20 children and six educators were killed in 2012, state lawmakers in Connecticut set out to draft some of the toughest gun measures in the country.

They largely succeeded — significantly expanding an existing ban on the sale of assault weapons, prohibiting the sale of magazines with more than 10 rounds and requiring the registration of existing assault rifles and higher-capacity magazines. The state also required background checks for all firearms sales and created a registry of weapons offenders, including those accused of illegally possessing a firearm.

Now, in the wake of another wrenching shooting rampage — this one at a high school in Parkland, Fla., that killed 17 — and in the absence of any federal action, gun-control advocates, Democratic politicians and others are pointing to the success of states like Connecticut in addressing the spiraling toll of gun violence.

Analyses by the Giffords Law Center to Prevent Gun Violence show that, with few exceptions, states with the strictest gun-control measures, including California, Connecticut, New Jersey and New York, have the lowest rates of gun deaths, while those with the most lax laws like Alabama, Alaska and Louisiana, have the highest. The center is named for former Representative Gabrielle Giffords, a Democratic lawmaker from Arizona who suffered a serious brain injury in 2011 during a mass shooting in which she was the intended target.