Perhaps CGI::Application::Dispatch is what you're after?
Have a look at the "Simple Apache Example" on its CPAN page for an example of how to serve files or directories directly, but route other requests to your dispatcher/cgiapp.
Comment on Re: CGI::Application::Authentication and Static Pages
I looked at using mod_rewrite rules to solve the problem, but I still need to use C::A::Plugin::Authentication to authenticate users, even for the ststic pages.
Thanks for the pointer to that sample. It is a great example of using mod_rewrite.