HJ's dashboard

Well, there's no way to sign out but you can add a new account, if you want to log in all the times you use this app you'll have to delete your account saved all the times you use the twitterrific.
To add a new account: once you log in go to Sources (on the up-left corner) then click on Edit (up-right corner) and then choose Add a New Account on the menu! Done!
To delete your account: once you log in go to Sources (on the up-left corner) then click on Edit (up-right corner) and then choose the first "-" red sign that is on the left side of your twitter name, click on Delete (the red sign), go to your iPhone menu and try to access again the twitterrific. Done!

I hope to help you... That's the only way to "sign out" from Twitterrific. At least that was the only way i found.

xx
HJ