A larger and uncropped copy of the poster has no copyright marks as shown in the link above.
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A check for copyright for works of art for 1935 and 1936 found no information.
Further checks for any possible renewal of copyright were done in artworks and photographs for the years 1963 and 1964, also with no results regarding the item.
On the basis of no marks on poster, no original or renewal registrations found, the license is changed to PD-No notice.
Note that it may still be copyrighted in jurisdictions that do not apply the rule of the shorter term for US works (depending on the date of the author's death), such as Canada (50 p.m.a.), Mainland China (50 p.m.a., not Hong Kong or Macao), Germany (70 p.m.a.), Mexico (100 p.m.a.), Switzerland (70 p.m.a.), and other countries with individual treaties.