OOP PDO Database Connection
Besides the already mentioned things I like to add a few of my own:

Connection charset
You should set the charset of the connection the be the same of your php files (and  definition when you use html):

Simply add , array(PDO::MYSQL_ATTR_INIT_COMMAND =&gt; "SET NAMES 'utf8'") after $this-&gt;pass

Coding Style

The naming of class variables shouldn't be all uppercase, so rename $DBH to $dbh.

Additionally I'd advice you the read the Coding Style Guide from the PHP Framework Interop Group which many php framework developers pay attention to lately.
http://www.php-fig.org/psr/psr-2/

There it says in Chapter 4.3 that you should put the opening curly brace of function on a new line.

User Input

As soon as some user input gets into your sql statement you should use parameterized queries, for example:

$stmt = $this-&gt;dbh-&gt;prepare("SELECT * FROM user WHERE passwort_hash = :passwort_hash");

$stmt-&gt;bindParam(":passwort_hash",md5($_POST['passwort']));
$stmt-&gt;execute();
...


This protects you against SQL-Injections.