Route 145 is the only signed Connecticut route I know of that, at one time, intersected... itself.

CT 145 History

In the 1920s, State Highway 145 was the number for the old Ousatonic Turnpike, much of which is now abandoned, on the northeast bank of the Housatonic River. The road went from Shelton to New Milford.

The modern Route 145 was commissioned in 1932. This is a strange one. The 1942 highway log describes the route as "from 3-way junction Conn. 145 in Westbrook clockwise to Jct. Conn. 144, Saybrook (now Deep River)".

What does this mean? Here's the route, all 10.86 miles of it, from, er, 12 o'clock onward:

In 1943 or 1944, Routes 144 and 145 were moved slightly, with Route 145 continuing to Route 80, now extending 11.47 miles.

In 1963, Route 145 was extended to Route 148, and the portion south of US 1 was deleted. The southeasterly leg became unsigned SR 625.

CT 145 Sources