Just thought I'd add some additional info and an illustration from a book in my library, Soviet Military Uniforms and Insignia 1918-1958 by O.V. Kharitonov
USSR P.C.D. Order No. 61 of March 10, 1938, (edited):
"A cotton panama hat was authorized for wear, along with a steel helmet, for personnel of troops and institutions of the Middle Asia, North Caucasas and Transcaucasus Military Districts and for units located in the Crimea.
The panama hat was made of light cotton khaki fabric, with broad brim semi-rigid sloping stitched brims (7 cm wide). The crown of the hat was made up of four wedges with twelve openings, three in each wedge. A red star diameter 7.5 cm was sewn onto the front of the crown. The panama hat had a red lining and a chin strap made of the khaki material.
Panama hats for motor/armour troops were made of steel-coloured material."