A non-resident would need a CT non-resident marine license to fish in CT's portion of LIS.

The Marine License FAQ explains all the particulars here:

http://www.ct.gov/dep/cwp/view.asp?a=2696&q=443060&depNav_GID=1630

What is a Marine Waters Fishing License (MWFL) and who is required to have one?
The Marine Waters Fishing License (also known as a Saltwater Fishing License) is an annual sport fishing license issued on a calendar year basis. Anyone age 16 or older, fishing (taking or attempting to take fish or bait species) from shore or from a boat in the marine district of this state or landing marine fish or bait species in Connecticut taken from offshore waters is required to have one.