Until 1932, State Highway 343 went straight west from Warehouse Point to East Granby, along the old Route 20. You can't drive there today, as Bradley International Airport is in the way.
The modern Route 343 was commissioned in 1932. It was one of only two route numbers in the 300s at the time, for number continuity with a connecting New York highway. (The other: Route 341.)
Until Route 364 was designated in 1963, Route 343 was the highest signed number (post-1932) in the state.
US 44 route swap proposed, 1959
A two-state proposal to redefine US 44 near the New York state line would have, if taken up, changed Route 343 from an east-west route into a north-south route.
In late 1959, the states of New York and Connecticut advised the American Association of State Highway Officials (AASHO) of their intent to reroute US 44 along safer, better roads in the vicinity of the state line. The change would make US 44 a bit more serpentine in Connecticut, but remove a long overlap with NY 22 and simplify navigation in New York.
From Lakeville, Conn., US 44 would follow today's Route 41 into Sharon, and then Route 343 into New York State to Amenia, to rejoin existing US 44. Route 343 would be redefined to cross into Connecticut using Route 41, then cross back into New York replacing Connecticut Route 4 (now Route 361), to end at Millerton, N. Y. New York state would reuse the 361 number for old Route 343 between Millbrook and Dover Plains; Route 361 would never have existed in Connecticut. The remainder of US 44 between Millerton and Lakeville would return to its previous designation before US 44 was created: Route 199. Not mentioned in the the application or related news articles: Route 199 in Roxbury and Washington would need to be renumbered; following common DOT practice, the new number would have likely been 299.
To sum up:
- US 44 west of Lakeville becomes Route 199
- Route 41 south of Lakeville is divided into US 44 and Route 343
- Route 343 west of Sharon becomes part of US 44
- Route 4(361) northwest of Sharon becomes part of Route 343
- Route 199 becomes (probably) Route 299
The plan originated in New York State, but opposition in Millerton, which the new US 44 would have bypassed, appears to have helped scuttle it. There was also some opposition in Sharon, where the new US 44 would have gone through. Many Lakeville and Salisbury residents, having dealt with state plans to build a US 44 freeway in the area, were wary of the proposal until it was made clear that only signs would be moved.
In the end, US 44 was not changed in the area.
Connecticut and New York proposed rerouting US 44 along Routes 41 and 343, which were better roads at the time. Diagram from Connecticut route change application to AASHO in 1959.