You can pass an already initialized database handler, store it inside the object and then reuse it at will. Here's a tested example.

#!/usr/bin/perl -w
use DBI;
use strict;
package Other;

sub new {
    my $class = shift;
    my $self = bless {}, $class;
    my $dbh = shift || return undef;
    $self->{dbh} = $dbh;    # store the dbh
                            # for future use
    return $self;
}

sub do_it {
    my $self = shift;
    my $query = shift;
    #
    # reuses the stored dbh
    #
    my $sth= $self->{dbh}->prepare($query);
    $sth->execute;
    while (my $row = $sth->fetchrow_arrayref()) {
        print "@$row\n";
    }
}

package main;

sub do_it_differently {
    my $db = shift;
    my $query = shift;
    my $rows = $db->selectall_arrayref($query);
    for my $row (@$rows) {
        print "<@$row>\n";
    }
}

my $dbh = DBI->connect("DBI:driver:database", # change it
    'username', 'password', {RaiseError => 1})
    or die "can't connect\n";

my $query = qq{select * from departments };
my $ext = new Other $dbh          # passes a dbh to an object
        or die "can't create\n";
$ext->do_it($query);              # calls a method that uses a stored 
+dbh

do_it_differently ($dbh, $query); # passes a dbh to a sub

$dbh->disconnect();
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