"Can i delete this for one key only (no particular where i need to retain this value for which key, just need once in any key)"

I made reference to that in my original reply:

"To keep the values unique for a specific key, without removing duplicates from the values of other keys, you'll need to clear the %seen hash for each arrayref value."

In this code:

for (values %$HASH1) {
    my %seen;
    $_ = [ grep { ! $seen{$_}++ } @$_ ];
}
[download]

Just move the "my %seen;" line out of the loop:

my %seen;
for (values %$HASH1) {
    $_ = [ grep { ! $seen{$_}++ } @$_ ];
}
[download]

Which, as the loop now only contains one statement, you can write more succinctly as:

my %seen;
$_ = [ grep { ! $seen{$_}++ } @$_ ] for values %$HASH1;
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I put that into the original code I gave you (along with your new HoA). Here's the output:

{
  "Alabama"    => ["Andalusia", "Anniston", "Clanton", "Eufaula", "Aub
+urn"],
  "California" => ["Barstow"],
  "New York"   => ["Amsterdam", "Coney Island", "Beacon"],
  "Utah"       => ["Layton"],
}
[download]

Which exactly matches what you have for "so my result hash should look like".

By the way, purely for academic interest, because I can't see that it gains you anything in this particular instance, if you're using Perl 5.10, or later, you could have reduced those two lines to this one:

$_ = [ grep { state %seen; ! $seen{$_}++ } @$_ ] for values %$HASH1;
[download]

I tested that: the output is identical. See state for more details.