> Sorry, there is currently no way to accomplish this.

Nor should there be... there is NO way that any site other than
Twitter should control my login status on Twitter.

Now to the OP's question:

> When I logged out from my application, I need to logout from
> twitter also.

What _you_ can do is before you "forget" the login state of your
application, delete an OAuth tokens you have for the logged in user...
then when they return to login to your application, the will not-yet
have Twitter OAuth tokens, so it will appear that they are not
associated with the Twitter account and will have to reauthorize.
You can safely keep the Tweep's user id and (less safely) screen name
and profile image url around if you want to keep some knowledge of
them...

Marc

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