I’m a section hiker and plan to finish the state of Mass next month (going south). I would like to spot and leave ahead my vehicle in CT or Mass (which ever is nearest and safest to the trailhead juncture. I know there is parking spots near there, but are they safe to leave a vehicle there for a week? Is there a POC in that area who would be willing to allow parking a private vehicle at their home for a small fee.
Nancy
If you go a little further (6miles) into Salisbury, CT there is a parking lot on Undermountain Road (GPS N41.59.645 W73.25.615) or checkout a parking lot in town.
I don’t know how safe they are though maybe you can ask people in town if they can recommend a spot. The town isn’t that big so you wouldn’t be adding too much walking once you leave the trail.
Old Goat
We used a spot twice last year, once for a day hike, once for a single overnight with no issues - no idea how it would be for longer.
It’s a small dirt road (East St in MA) - goes by the Mt. Washington State Forest HQ - and the parking is just about on the state line - probably the closest you’d get since the line on the trail is around Sages and there is no access point right there.
If you are hiking the AT south, you’d cross through Sages Ravine, climb out of the ravine and start heading towards Bear Mtn, and there is a short trail to your right that brings you out to this spot. If you get to the top of the mountain you went too far 
On the way out the side trail you pass a cabin, so there is likely traffic in and out occasionally, but the road itself only accesses a few houses before the parking area so likely not a lot of traffic (and I’m not sure it goes through anymore past the parking areas, so that would cut traffic also).
Only consideration - we were there the first week in May last year and it was OK, but with more snow this year and since you are going in April it could still be soft/muddy (as it is a dirt road during the spring).
Billy