as per the suggestions by perlCrazy, I think a possible thread safe re-write of above code can be

use threads;
use DBI;



$SQL_1 = "SELECT * FROM x";
$SQL_2 = "SELECT * FROM y";
$SQL_3 = "SELECT * FROM z";

sub start_thread {
    my ($SQL) = @_;

    my $dbh = DBI->connect( <your connection string> );

    # print('Thread started: ', SQL, "\n");

    my $sth = $dbh->prepare($SQL);
    $sth->execute();

    < Add your code here >

}

 my $thr1 = threads->create('start_thread',  $SQL_1);
 my $thr2 = threads->create('start_thread',  $SQL_2);
 my $thr3 = threads->create('start_thread',  $SQL_3); 

$thr1->join();
$thr2->join();
$thr3->join();
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