FWIW, while it's not definitive, the label shown was introduced June 1960. If anyone has copies with the 1959 starburst label or the earlier maroon and silver label, that would help pin it down
The catalog number of the single release is solidly in the 1960 sequence.
Maybe I should go over to Joel Whitburn's office and see if they know (It's about three miles from my house) :-)
On the other hand, the listing of RW's charting LP's (this wasn't one) in Joel Whitburn's TOP POP ALBUMS suggests that this number falls into Kapp's 1960 releases, so...????
Paul Pelletier's RECORD INFORMATION, Issue Two, has June 1959 as the issue date of the UK mono edition (London HA-R 2169) and September 1959 for the stereo edition (SAH-R 6033), so it is quite possible that the US date was several months before that.
British release says "first published in 1958" yet "Both Sides Now" lists release date as 1960 for both single discs and 2 record set. (although I would believe it if the set did come out earlier)