This sounds like a follow-up to Perl DBI: Overloading statement handle. If so, can you post the code that you finally came up with. Actually, even if it's something completely different, still post the code.

Also, can you run print Dumper($dbh);, and post that output too.

I did have a similar problem that was very much like this. Using Dumper against $sth/$dbh is normally futile because the data is hidden behind a tie(). In cases of subclassing Perl's DBI, you'll laugh, you'll cry, and you may want to consider callbacks instead.
http://search.cpan.org/~timb/DBI/DBI.pm#Callbacks
Ken, I'll go back to the Perl DBI question I had previously and post what worked for me.

A stackoverflow answer:

print Dumper tied %$dbh;
[download]

Thanks for that link. print Dumper($dbh) has almost the same result.

$VAR1 = bless( {}, 'DBConnect::db' );
[download]

I am starting to think that Dumper just won't work on DBI.

I would say it's working perfectly fine. I can achieve the same output with that code:

$ perl -wE 'use Data::Dumper; my $dbh = bless {} => q{DBConnect::db}; 
+print Dumper($dbh);'
$VAR1 = bless( {}, 'DBConnect::db' );
[download]

But, the real question is: What's your code doing?

-- Ken