Automatic logon to Windows Forms App using current user Windows credentials

Question

I have written an application that is run on a Windows terminal server on connection. This functionality is provided by the Microsoft terminal services client. My application has its own user database and this is synchronised with the Windows domain database so that when a user logs on to my application the application uses the Win32 LogonUser function to verify the credentials entered against the domain.

Is there a way I can get Windows to pass the user credentials to my application at application start up to achieve single sign on?

What I mean is the user has already entered their credentials and had them verified to logon to the terminal server, as soon as they connect my application runs and they are asked for the same credentials that they just entered again in order to logon to my application. If Windows could pass them in automatically it would be a lot slicker.

Can it be done?