It's probably coincidence, but Route 244's number hints at its optional role as a bypass to US 44 in Eastford and Pomfret. A 3.1-mile section from Route 97 to Chase Pond Road is a state scenic road.
Also, 244 is Connecticut's newest signed route number: before its designation in 1988, it had never been used for any route before. Among other "new" routes: I-691 appeared in 1987; I-291 was preceded by State Route 291; and Route 130's number first appeared in the 1920s.