How can we implement Sign Out in MVC application using windows authentication ?

Mozilla explicitly that you cannot close a window with script that wasn't opened with script[^].

Chrome is version dependent, but some hacks can close the window. It's a 20% option, though, so rather than do that pick a method that will work for all browsers.

Your better option IMO is to clear the cookie and redirect to another site; if you have an internal landing page that's a good choice.

There's a solid example of how to quickly and easily blow your cookies up here.[^].