Route 31A existed only a year, as the short road named Depot Road and Coventry Road, between Route 31 in Coventry and Route 32 in Mansfield. This was formerly the southernmost segment of Route 31. This Road had many unsafe features (curves and narrow bridges); in 1935, local officials asked the state to move the primary highway (US 6 at the time) to a new alignment.
In 1947, Route 31 was moved to the Main Street / Higgins Highway diagonal route leading toward Willimantic. The old segment of Route 31 became Route 31A.
In 1948, Route 31A was cancelled and Depot Road was turned over to the town. A street survey document from the Town of Mansfield has a filing date of July 26, 1948, street name "Route 31A", description "Section of Highway to be Abandoned."
I don't know if Route 31A was ever signed. I've never seen it on a map.