Build EGit repository outside Eclipse workspace

I use Eclipse 3.7 and EGit 1.0. If I create repositories inside my Eclipse workspace (as a sub-folder for a project) everything works fine. But obviously this is not recommended so I want to build a repository in a place elsewhere. But this does not work as expected.

I make this steps:

1. Create a simple Eclipse project with a text file in it (myproject).
2. Share -> Team -> Git
3. Create Button -> use c:\user as Parent Directory and mygit as Name
4. I leave Path within Repository empty
5. so Target Location is c:/user/mygit/myproject -> Finish

At this point I expect that I can manage my code via EGit. But if I choose the Team menu within the project or text file context menu I see no version control options like commit etc. On the other hand if I delete the created repository the project is also deleted.

Does anybody know how to do this correctly? At first my goal is to build a simple single user repository.