A few minutes ago, I did a quick search and found it right away. The book is based on his childhood. Titled Little Leo, here's the cover:
It was published in 1951, three years after Song of the Swallows. I think I have it somewhere... A good friend sent it to me a few years ago. The image above is from Appleby Books, a source for collectible and rare books. Their description:
A story based on Leo Politi's own childhood. Little Leo loved watching the Indians in the movies and one day his father bought him his own wonderful Indian Chief suit. When little Leo and his family traveled to his father's village in Italy, all the children were enchanted with Leo's suit and wanted to be Indians too!It is fascinating to think of the Leo-Politi-the-man writing about primitive Indians in Song of the Swallows, knowing that Leo-Politi-the-boy played Indian!