I'm thinking about becoming a CT State Trooper...
I researched their website. What should I expect in terms of the day to day responsibilities?

It's a long process to get hired.  After the academy, where they drill the "trooper mentality" into your head, you have a less than exciting career in traffic enforcement.  This is a generalization, you can get all sorts of stuff on the highway.  Resident troopers,  and the occasional deployment to Hartford may spice things up.  Some love it, some like working in a larger city or town.  Pay is OK, but some town cops who subsequently went to the state, regret the pay cut and slower pace.  
This past Saturday, there was a 10 car pile-up on I-91 N.B.,  that was enough to make me feel glad I work in Hartford.  
It is up to you and what you want to do.  You have the benefit of a quick respone time for your back-up if you work in a municipal P.D.  The shiny take home car is nice, but if you are driving it off duty, you are required to provide assistance/take action if you are needed.  State-wide jurisdiction is cool, but, you may be posted at a troop an hour away from your residence.  IM me if you have any specific questions.