In current version of Zencart the state dropdown does not seem to appear. I believe I traced it to the checkout_new_address.php module line 32 appears to be missing

$check_query = $db->bindVars($check_query, ':zoneCountryID', $country, 'integer');

Missing Line should be -> $check = $db->Execute($check_query);


$entry_state_has_zones = ($check->fields['total'] > 0);