There is a button to disconnect your Facebook account from Duolingo, but none for Twitter.
I am bringing this up because I accindently attached my Duolingo account to the wrong Twitter account and had a difficult time fixing my mistake. Had to do it through Twitter's website.
On the "Follow people" page on the duolingo site, click "Search again on Twitter" and a window should pop-up. Click "sign out" in the upper right hand of the pop-up window. Then you should be able to enter the correct account credentials and click the "Connect" button. This should fix your problem, but if it does not, click "Search again on Twitter" and click the "Connect" button.
Hope this helps.