$dbh = DBI->connect($db_datasource, $db_user_name,
                    $db_password)
  or die("Could not connect!".$dbh -> errstr);
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If the connect call fails then $dbh will be undefined (i.e. it will contain the value "undef") - so trying to call a method on it will be doomed to failure.

In this case you want to access errstr as a package variable.

$dbh = DBI->connect($db_datasource, $db_user_name,
                    $db_password)
  or die("Could not connect!" . $DBI::errstr);
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Update: Maybe you should have tried checking the DBI documentation as the examples for connect show this usage.