my %data;

{
   my $in = 0;
   my %rec;

   while (<DATA>) {
      if (/^\s*{/) {
         $in = 1;
         next;
      }

      if (/^\s*}/) {
         my $name = delete($rec{Name});
         $data{$name} = { %rec };
         undef %rec;

         $in = 0;
         next;
      }

      if ($in) {
         if (/^\s*(\S+)\s*=\s*"(.*)"/) {
            $rec{$1} = $2;
         }
      }
   }
}

require Data::Dumper;
print(Data::Dumper::Dumper(\%data));
[download]

outputs

$VAR1 = {
          'C:' => {
                    'Size' => '160031014912',
                    'FreeSpace' => '114151464960'
                  },
          'D:' => {
                    'Size' => '203921108992',
                    'FreeSpace' => '5515554816'
                  },
          'H:' => {
                    'Size' => '400086708224',
                    'FreeSpace' => '43128733696'
                  }
        };
[download]

You could also use the .. operator:

my %data;

{
   my %rec;

   while (<DATA>) {
      if (/^\s*{/ .. /^\s*}/) {

         if (/^\s*{/) {
            next;
         }

         if (/^\s*}/) {
            my $name = delete($rec{Name});
            $data{$name} = { %rec };
            undef %rec;

            next;
         }

         if (/^\s*(\S+)\s*=\s*"(.*)"/) {
            $rec{$1} = $2;
         }
      }
   }
}

require Data::Dumper;
print(Data::Dumper::Dumper(\%data));
[download]