The whole thing looks kinda OOP. Why not hang the DB connection in your object. Passing it around through all these routines as a parameter is a waste of namespace, and it makes your coupling to tight. If you have an OO interface, you could do something like

sub SomeDBRoutine {
  my $self = shift;
  $obj->dbh->WhatEver;
}

sub dbh {
  my $self = shift;
  if ( @_ ) {
    $connection_string = shift;
    $self->{dbh} = DBI->Connect($connection_string, "user","pass");
  }
  return $self->{dbh};
}
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This way you let the module control the connection and you can quite easily set a connection or use it.

Did I mention that this code is untested...?

Sinister greetings.
"With tying hashes you can do everything God and Larry have forbidden" -- Johan Vromans - YAPC::Europe 2001
perldoc -q $_