Route 31A existed only a year, as the short Depot Road between Route 31 and Route 32 in Coventry. This was formerly the southernmost segment of Route 31. Depot 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. Depot Road became Route 31A. In 1948, Route 31A was cancelled and Depot Road was turned over to the town.
I don't know if Route 31A was ever signed. I've never seen it on a map.