Thanks Huck and Keybot . From your solution, It is clear to use md5dum's as the keys of the hash and then hash value as a reference to an array of files . I have changed my original code to create a Hash of an Array to do this.

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dumper;
##############
my $dir = "$ARGV[0]";
my %md5sum;
opendir(my $dh, $dir) || die "Unable to Open the Directory: $!\n";
chdir $dir or die "Cannot Change directory: $!\n";
while (my $file = readdir $dh) {
    chomp $file;
    next if $file =~ /^\.{1,2}$/g;
    if (-f $file) {
        my ($md) = (split /\s+/, qx(/usr/bin/md5sum $file))[0];
    if (exists $md5sum{$md}) {
       push @{$md5sum{$md}}, $file;
    } else {
       push @{$md5sum{$md}}, $file;
    }
  }
}
   closedir($dh);

foreach my $ky (keys %md5sum) {
    if (scalar( @{$md5sum{$ky}}) == 1) {
       print "Unique File: @{$md5sum{$ky}} , Md5sum: $ky\n";
    } else {
      print "Duplicate Files:  @{$md5sum{$ky}}, Md5sum: $ky\n";
    }
}
[download]

-bash-3.2$ ./duplicate_files.pl directory
Duplicate Files:  file4 file2 file3, Md5sum: d41d8cd98f00b204e9800998e
+cf8427e
Unique File: file6 , Md5sum: d617c2deabd27ff86ca9825b2e7578d4
Duplicate Files:  file1 file5, Md5sum: 5bb062356cddb5d2c0ef41eb2660cb0
+6
[download]