Sony's release chronology included in the Original Mono Recordings box set gives the single's release date as March 27, 1967, the same date as Greatest Hits.  However, Dylan's Contract Card as reproduced in the CD-carrying book of The Cutting Edge 1965-1966 (6-CD Deluxe Edition) indicates (behind Disc 3) that single 4-44069 shipped on 24 April 1967.  This later date ties in with its release in other countries, and is more likely to be correct.

Dylan's Contract Card, page 31


Further evidence comes from a promotional copy of the single which was apparently sent in 1967 to WCCS, a college radio station in Connecticut, and put up for sale on eBay in 2020. The 4/25 written on the label suggests that it was received by the station on April 25, 1967.

Radio station promo with 4/25 date on label