calling mysql_close() in order to close the mysql-connection and kill the mysql-process dont work. calling mysql_close() a second time closed the connection. 
mysql_close(link_identifier) doesnt work. doesnt matter how often i called it.

i tested it with a little script:

$con=mysql_connect("localhost","***","***");
$result=mysql_db_query("chat","select * from chat",$con);
mysql_close();
while($i<10){
    echo "$i <br>";
    flush();
    sleep(1);
    $i++;
}

if you now make a mysqladmin processlist you see a process wich is sleeping for 10 seconds. 
when the scripts ends the mysql-process is gone. 
the same script with calling mysql_close() two times lets the mysql-process go away right as i expected. mysql_close($con) never worked. 
calling mysql_close() a third time produces an error message. calling first mysql_close($con) and then mysql_close() does nothing, too. 

mysql-server-version is 3.22.32