You could just check if the key is blank

#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;
use Text::CSV_XS;
use IO::File;

my $hash_ref = csv_file_hashref('parameters.conf');

foreach my $key (sort keys %$hash_ref){
  print $key.':';
  print join ',', @{$hash_ref->{$key}};
  print "\n";
}

sub csv_file_hashref {
  my ($filename) = @_;
  my %output_hash = ();

  my $csv_fh = IO::File->new($filename, 'r');
  my $csv = Text::CSV_XS->new( { allow_whitespace => 1 } );

  while (my $row = $csv->getline($csv_fh)){
    my $key = shift @$row;
    next if $key =~ /^#/;
    if ($key =~ /\S/){
      $output_hash{$key} = $row ;
    }
  }

  return \%output_hash;
}
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Note $item =~ /^\s+$/ matches 1 or more white space only (but not nothing). Try $item =~ /^\s*$/ in your code.