As the other Monks already stated, this is a problem related to how Apache is configured, not to perl or mod_perl.

So, you can move your file out of the way, so it's not in the dir (or in any subdir) you have set up Options ExecCGI in. Or you can add a rule like RemoveHandler .css to that very same directory. As I've personally never gotten that last one to work, you can, as a last resort, create a style directory and set it up with SetHandler none using a <Directory> or <Location> directive.