auto trans?

is it possible to install dohc vtec auto tranny on a sohc vtec engine?

I'm pretty sure there isn't such a thing for the 6th gen Civics (DOHC auto tranny). The Civic SI's came from the factory w/ the DOHC engine and manual tranny. Just as I'm almost positive you can't put an automatic tranny, say from an EX, onto a DOHC engine. Someone correct me if I'm wrong.