Above: GFS 500 mb (mid-level) forecast for 1 A.M. Monday, with surface low track superimposed (red arrow).
At this time the odds favor most of Connecticut not seeing measurable precipitation for the next 9 days. There have been some snow showers/flurries in western Massachusetts this morning, and you might run into a flurry in some of the northwest hills - but nothing of consequence. The next chance for any type of precipitation appears to be Thursday night when a reinforcing cold front moves across the region. This front could produce a flurry or snow shower, however it will have little moisture to work with, so most of the area probably won't see any measurable precipitation. After that, the next chance for precipitation would come during the Sunday/Monday time frame, but at this time that looks like a long shot. An area of low pressure moving across the southern U.S. later this week will most likely be ushered out to sea by the southern branch of the jet stream far enough to our south & east that we do not receive any precipitation from it. Most model solutions support this scenario with the exception of the GEM (Canadian model). There are also a couple members of the 21 member GFS ensemble that bring the northern fringe of the precipitation into Connecticut, so it's not that there's no chance for it to happen - but the odds are against it right now. Otherwise the next 9 days look dry & cold with highs mostly in the 30's and lows in the teens & 20's. Parts of the state could touch 40 degrees Thursday before the cold air reinforcement arrives Thursday night/Friday.
UPDATE: The new run of the GFS-FV3 (more advanced, but still experimental version of the GFS model) just came in while I was writing this. It brings the northern fringe of the precipitation further north than the previous run. Still pretty far out in time, so it might give us something to look at over the next couple days.
Below: Latest run of the GFS-FV3 forecast for Sunday night.