You are checking the $key, which is always a string. You should have been checking the value corresponding to the key:

    for my $key (keys %$decodedJSON)
        {
            if (is_hashref($decodedJSON->{$key}))    {
                print "$key is another hash\n";
            }
            elsif(is_arrayref($decodedJSON->{$key})){
                print "$key is an array ref\n";
            }
            else{
                print Dumper($key);
                print "$key is neither a hashref nor an arrayref\n";
            }
        }
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