Has the back strap, silk soft roller inside. This hat is probably from around the Korean War make judging by the plastic lining, but is certainly vintage (the assistant principal of my high school bought one just like this at the PX when he was recalled during the Korean War). It came from the private collection of the person that ran Globe Militaria, and has been in my own collection for about 30 years.
The hat badge is a replacement, and it fits very well over the shadow of the officer's badge that had been present. Fantastic shape with a few pinholes in the top cover, see scan for close-up. Small size, probably was a size 7 or so before shrining a little like all vintage hats. Original owner's name and service number inside hat.