When the record ("Over The Rainbow") made it's first appearance in Billboard, it was in May of 1960 as a Review, and then known only as by the Demensions. When LAURIE Records bought the masters in June, they kept it on MOHAWK, but changed the spelling to the Dimensions. The outward sign of the two issues was the label styling. The original "e" release was on the then current red label. When it was re-issued with the "i", the label styling went out of normal with a maroon label and a different look altogether.
If you are filing because of it's Chart value, the spelling should be as The Dimensions, since that's the way it was at the time.