You should store a database handler into your object property:

sub DB_connect
{
    my $self = shift;
    $self->{dbh} = DBI->connect( DBI_STRING )
        ||    die "Cannot connect: $DBI::errstr\n";    
}

sub DB_finish
{
    my $self = shift;
    $self->{dbh}->disconnect;
}
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For understanding Perl OO, please see Tutorials::Object Oriented Perl.
If you need to have a superstructure over DBI, it's enough to make it as module not necessary to create a class.

      
-------->
SV* sv_bless(SV* sv, HV* stash);
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