The Brady Campaign gives Connecticut high grades for its gun laws

It ranks the state 5th of all 50 states.

http://www.bradycampaign.org/stategunlaws/scorecard/CT/

I have not seen any reports that the shooter's mother circumnavigated Connecticut laws by going to other states.

The NRA appears to have little influence in Connecticut. Just a small fraction of the total amount the NRA Super PAC spent in 2012 on political donations went to campaigns in that state.

"Though the NRA has not had good success in Connecticut's congressional contests, at least 15 sitting members of the state legislature received contributions from the NRA.....Since 2010, the NRA has reported spending $8,000 on lobbying at the state, records from the Office of State Ethics show,....On the federal level, the NRA has spent more than $2.2 million on lobbying on issues from firearms, right to bear arms and on homeland security issues."

http://reporting.sunlightfoundation.com/2012/connecticut-shooting/

The governor is a Democrat, Governor Dan Malloy, and Dems have a large majority over the Repubs in both chambers of the General Assembly.

"Members of the General Assembly, regardless of chamber, serve two-year terms; there are no term limits imposed on them. The 2011-2013 House is made up of 52 Republicans and 99 Democrats, while the 2011-2013 Senate has 14 Republicans and 22 Democrats."

http://en.wikipedia.org/wiki/Connecticut_Legislature#Membership

There doesn't appear to be been much impediment to Connecticut passing stricter gun laws that may have prevented this tragedy. On the other hand, passing legislation on a federal level that would match the gun control laws already in force in Connecticut would be a huge undertaking. Especially when one considers that the House is controlled by the Repubs.