I think the Perry Como version was based on an older song sung at camps and such. Here is one version.

What Did Delaware, Boys?

Oh, what did Delaware, boys? Oh, what did Delaware?
Oh, what did Delaware, boys? Oh, what did Delaware?
Oh, what did Delaware, boys? Oh, what did Delaware?
I ask you now as a personal friend, what did Delaware?

She wore her New Jersey, boys. She wore her New Jersey.
She wore her New Jersey, boys. She wore her New Jersey.
She wore her New Jersey, boys. She wore her New Jersey.
I tell you now as a personal friend, she wore her New Jersey.

Other verse pairs include:

Oh, what does Iowa? She weighs a Washington.
Oh, what does Idaho? She hoes her Maryland.
Oh, what does Tennessee? She sees what Arkansas.
Oh, where has Oregon? She's gone to Oklahoma.
Oh, what did Massa-chew? She chewed her Connecti-cud.
Oh, how did Flori-die? She died in Missouri.
Oh, how did Wiscon-sin? She stole my New-brass-key.