The north-south section of Route 188, serving Quaker Farms, Southford and Middlebury, is conventional and straight by Connecticut standards. The east-west section, sort of an appendage, diverts eastward from Route 64 – the two routes intersect but do not cross – and crosses I-84 again, with no interchange, before ending at Route 63.
Route 286 does something similar in Ellington, though it doesn't quite intersect Route 140 (Ellington's Route 64 in this analogy) at all.
The portion of Route 188 near I-84 was in 1998 a growing office park area. (This fact was mainly included so I could cite a newspaper article with "Route 188" in the headline.)
CT 188 History
Route 188 was created in 1935, following today's route between Route 34 and Old Waterbury Road, former Route 135. There's a mismatch between the old definition of the route in the highway log (9.21 miles) and the actual length between those two points (10.3 miles).
Part of the original Route 188 had been state maintained earlier: SR 470 in Oxford, which appears to have been Quaker Farms Road from Barry Road to Plaster House Road; and SR 504 in Oxford and Southbury, probably close to Route 67.
In 1935, the Southford Road and Whittemore Road sections of future Route 188 were still part of Route 135, at the time a fairly important connector from Southbury to Waterbury. The Route 135 corridor is now served by a freeway: Interstate 84.
Circa 1943, Route 135 was decommissioned. Route 188 was extended northeast and east over part of the route; the rest of Old Waterbury Road leading to Southbury, was turned over to the town.