Most of the information I was able to find from that error comes from 'Institute for American Indian Studies" at this site It looks like they are affiliated with the Peabody Museum of Natural History at Yale University, which says something to their credibility.

I also found this document through Google Scholar. Page 27 has information from the time frame you're looking for: "Middle Woodland Period (A.D. 1–1000) The Middle Woodland people appear to have continued to live in much the same way as the Early Woodland people. They used similar point and pottery styles and apparently practiced the same subsistence activities and seasonal round. New point and pottery types did make an appearance, however. The point types include medium-bladed, lanceolate or wide-stemmed, concave base Fox Creek points; lanceolate Greene points that taper to a rounded or straight base; and thin, medium-bladed, corner-notched and pentagonal Jack’s Reef points. There are no published dates for these points in Connecticut. In New York, New Jersey, and Massachusetts, however, Fox Creek occupations characterized by Fox Creek and Greene points have been radiocarbon dated to the early Middle Woodland—be- tween A.D. 325 and 605. Jack’s Reef points have been dated to the late Middle Woodland Period at New York and New Jersey sites—between A.D. 630 and 955."

So it appears that there was habitation in the Connecticut region during your time frame.

Let's start with the easy one: yes, there were people living in Connecticut in 256 CE. Who were they? Now that's the hard part. Archaeologically, they're known as the Windsor Tradition, but this is a sort of wastebin taxon of archaeological artifacts. If you find an artifact (especially ceramics) from southern New England and it dates anywhere from 3000 years ago to around 500 years ago, it's Windsor. Of course, the Windsor tradition isn't some unchanging monolith, and is subdivided into numerous phases. At this time period, we're looking at either the late North Beach phase or the early Clearview phase (or if you like to split the phases up a bit more, we're squarely in the Fastener phase.

Regardless of what we call the phase, there's not a lot that can be said with certainty. At this time, Connecticut is sparsely populated and isolated from the larger trends of the period that are happening across the Hudson and continuing on all the way to the Mississippi and beyond. Trade goods from outside southern New England are virtually non-existent, as is evidence for horticulture / agriculture. People may have been cultivating things like sunflowers, sunchokes, and goosefoot but it doesn't appear to have made up a sizable portion of the diet and the strongest evidence for such plants comes from a bit later. Instead, people are moving in small family groups between seasonal camp sites, particularly between coastal fishing camps and interior harvesting and hunting camps. It'll be another 200 years before people in the area start gravitating toward large riverside village sites - a trend that will accelerate rapidly with the adoption of maize around 900 CE.

As for the Adena, 250 CE is a bit too late for them. By this time, even the Adena traditionalists in eastern Ohio and West Virginia had assimilated into the larger Hopewell tradition (as the Armstrong Hopewell). By 250 CE, the various local expressions of the Hopewell tradition were running the show from upstate New York to Kansas City. As mentioned, the Windsor tradition was largely left out of the loop on the whole Hopewell enterprise. But, for the record, at least some people in Connecticut had contact with the Adena at one time. There are very few Adena-affiliated sites in New England, but one of them - the East Windsor Hill site, is perhaps the clearest. Not only does it look like a typical Adena burial (extended body in a conical mound with grave goods, contrasting with the typical bundled reburials that were otherwise common at the time), among its artifacts was a piece apparently from Flint Ridge in Ohio. Unfortunately, I haven't been able to find a date on the East Windsor Hill site, so I'm not sure how much (presumably) earlier it would have been. Another possible Adena-affiliated site was found in Milford, CT, though this one is less certain. It has tear-drop shaped blades similar to those manufactured by Adena-related groups in New York, made from a non-local chert (source unknown).

For more information, I recommend checking out the Archaeological Society of Connecticut's bulletins. Number 62 was particularly helpful with this post. I also drew a bit from Dean Snow's Archaeology of New England.