You could reverse the logic of your sub:

if ($file) {
    open LOGFILE, ">>$file" or die "Error message: $!\n";
} else {
    open LOGFILE, ">&STDERR" or die "Another error\n";
}
print LOGFILE "blah blah";
close LOGFILE or die "Yet another error\n";
[download]

-- TMTOWTDI