You May Be A Doggone Dangerous Girl But I'm a Desperate Guy
(Click on image for a larger version)
The "Desperate Guy" in on the cover of this 1918 piece of sheet music is "Little Billy" Rhodes, best known as the Barrister in The Wizard of Oz and (for you bad film aficionados) as the bad guy in Terror of Tiny Town. Looks like he had quite the career until the early 1940s or so.
I've no idea whether or not the signature is genuine, but it's an interesting addition to the ephemera collection.
The co-lyricist is Arthur Freed, a lyricist who went on to co-produce The Wizard of Oz and from there produce many of the outstanding MGM musicals.