Check out Green Mountain Practical Shooters http://www.gmps.ws/
They have hosted some of the biggest USPSA matches in the NE. Great bunch of shooters. I am not sure if they have three-gun or tactical rifle matches but I bet any of their contacts could point you in the right direction. Also: I shot the Area7 match up there last summer. Their club's ranges are absolutely the most beautiful I have ever shot at.
The range Whitey mentioned is Lamoille Valley in Morrisville. It is really nice but a bit of a drive from Burlington. The contacts on their club webpage would be good people to ask. http://www.gmps.ws/
I would also ask around at the Powder Keg, which is the gunshop at the end of Williston Rd, near Home Depot, or Parros in Waterbury.