Looks like Zoll, based on the cloth the hat is made from. It would be for a mid-range officer based on the silver piping along the top edge. The cockade, however, isn't Zoll as far as I know. Hmmm... I think it's Bayern? Didn't they used to have Grenzpolizei for a small period of time?
Edit. Just checked and memory does serve me correctly, I think! This hat is most likely Bayerische Grenzpolizei from very early 1960s. Here's a picture I found a while ago of historical Bayern uniforms (huge picture on this page.
"This hat is most likely Bayerische Grenzpolizei from very early 1960s."
Yes, and
"The hat is probably very rare."
Yes.
To my knowledge this type of material (similar to the early LW Fallschirm smock material - maybe it was?) was only used in the late 1950's/early 1960's. If the kokarde is original to the cap, this is quite a 'score'.
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