There's a sound clip of the song (the first verse minus the title line) here

Supposed to be an audio file here, but I couldn't get it to work
 

here issome interesting info/opinion) on Sinatra and what he aimed to accomplish via this song.
and here

All the sites I visited listed the composers as (Lewis) Allen, lyrics and Earl Robinson, music.  This seems to be accurate, since Lewis won awards for the song/film, along with the others involved.  I don't know why the first site I saw gave Millard Lampbell as the lyricist.  Research is needed.

The 1945 movie The House I Live In here won a Golden Globe as the best "Motion Picture Promoting International Understanding"  Mervyn LeRoy directed it  and apparently won some kind of Oscar, too  Seems the Oscars honored LeRoy, Sinatra, Allen, Robinson, Frank Ross, RKO Radio, and Albert Maltz for "Special Achievement" for that 10-minute film.

Info on Earl Robinson  is here.
 
 

Joe, you beat me to posting the full text of the Sinatra version, but here its is, with the intro and, I believe, with the authorship corrected:

The House I Live In
w: Lewis Allen; m: Earl Robinson
Performed By Frank Sinatra
In the motion picture  "The House I Live In," A documentary

What is America to me--
A name, a map, a flag I see?
A simple word, "democracy?"
What is America to me?

The house I live in, a plot of earth, a street;
The grocer & the butcher & the people that I meet;
The children in the playground, the faces that I see-
All races, all religions, that's America to me.

The place I work in, the worker at my side;
The little town or city where my people lived & died;
The 'howdy' & the handshake, the air of feeling free.  -
The right to speak my mind out, that's America to me.

The things I see about me, the big things & the small.
The little corner news-stand & the house a mile tall;
The wedding in the church yard; the laughter & the tears;
The dream that's been a growin' for more than two hundred* years.

The town I live in, the street, the house, the room.
The pavement of the city or a garden all in bloom;
The church, the school, the clubhouse, the million lights I see;
But especially the people, that's America to me!

* Original 1945 lyric "...for a hundred fifty years."
 

You may want to delete my first paste of the song and stick this one in in its place. I know that on NPR a few years back, I heard a longer version done by Paul Robeson, and they said something about his doing the song in a film.  The one you posted, Joe, is probably the version that Robeson sang. It could be I confused "Earl Robinson" with "Paul Robeson," but I could swear it was Paul Robeson's rather distinctive voice I heard. Do you know anything about a film version in which the song was sung by someone other than Sinatra?

Genie