This interesting historic account was brought to us by Cryptomundo and the letter 'H'
Catch Strange Animal
Hopping Along Highway
Washington, Pa., Aug. 22 (AP) – An “animal without a name,” which goes for vegetables and nuts in a big way, had the townsfolk puzzled today. No one could identify it.
The “watcha-call-it” has been viewed by hundreds since Saturday, when, hopping along the road like a kangaroo, it was corralled by a group of men and boys.
Its rear legs are like a kangaroo’s, its head and ears resemble those of a squirrel, and the eyes and nose bring to mind a rabbit. Its hair varies from brown to green.
Game Protector Carl Stainbrook is investigating whether the animal escaped from a carnival sideshow.
“I never saw anythink (sic) like it,” he said. “I searched through a book on the mammals of America and can’t find anything like it.”
Source: Reading, Pennsylvania
August 22, 1939
Without knowing the size of the animal or much else, it's hard to speculate on what it could have been. My top contenders, however would be: Ornate Tree Kangaroos, Wallabies, and Pademelons.
Of these, a Pademelon is the most squirrel-like.