I'll just pretend the 3rd "my" in your code isn't there. Others have already pointed it out...

One may still perform a variety of operations on the hash reference (and consequently the hash itself). Is this correct?

Yes, and that's why this isn't a memory leak :-) Java has the same behaviour in this case: if you can get at it, it's kept in memory.

To reduce the reference count to 'zero' (eliminating any potential memory leak that is present), I could simply set the $hash_ref variable to 'undef'(?)

You could. You could also let the reference go out of scope, and it will be cleaned up automatically. The only problem with a reference counting garbage collector are circular references. Like this:

   { 
     my %monks = ( 
                   Zaxo      => 'W. Virginia',
                   tye       => 'California',
                   theorbtwo => 'Germany',
                   castaway  => 'Germany',
                   atcroft   => 'Georgia',
                   rozallin  => 'England',
                 );
      # %monks has a reference count of 1

      my $ref = \%monks;

      # $ref has a reference count of 1
      # %monks has a reference count of 2

      $monks{myself} = \%monks;

      # %monks has a reference count of 3
   }
   # leaving the scope decrements the reference count
   # for %monks and $ref by one.

   # $ref is collected (has a refcount of 0) 
   # - decrement the reference count for monks 
   #   by one again

   # "%monks" has a reference count of 1
   # and is not garbage collected
[download]

The reason %monks is not collected is because there still is a reference to %monks in $monks{myself}. $monks{myself} would be removed if %monks were collected, but there is still a reference to %monks in $monks{myself}... etc...

A mark-and-sweep collector can detect these circular references and would also collect %monks here. Perl doesn't (except at the end of execution).

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