There is no secure-way to automatically do it, I implemented an application with local account/Twitter.Facebook/Google and I didn't have other choice.
I suggest you to allow your users to register with one method (local account, Twitter, Facebook, Google...) and create a page in "My account" that allow them to associate other accounts.
In Twitter a user can be identified by either a name or a key, you have no way to know them unless you explicitly ask them to the user.
Moreover now in Twitter 1.1 you have to redirect your user to Twitter to approve your application and then you get the OAuth token and security key. As you can see there must be an interaction with Twitter, at least if you need to perform some restricted queries on his behalf (e.g. create a Tweet).