I may be missing the point here...

Since you seem to be using global variables anyway, you don't need to even return anything from build_list.

You are passing in references to hashes. Those hashes are being modified by build_list. Your assignment to the hashes from the return value of build_list is redundant. They are already modified when build_list returns. Just use %RECORDxRI_count and %EACH_RECORD.

I assume you are doing more in build_list and the <DATA> loop than you actually posted...

Here is some condensed code (since you expressed interest in minimizing lines of code):

my %RECORDxRI_count;
my %EACH_RECORD;

sub build_list {
  my( $RECORD, $RI, $RECORDxRI, $RECORDxRI_count_REF, $EACH_RECORD_REF
+ ) = @_;

  $RECORDxRI_count_REF->{$RECORDxRI}++;
  $EACH_RECORD_REF->{$RECORD} = '';
}

while <DATA> {
  my( $Record54, $Record38 ) = (split /\t/)[54, 38];

  my $RECORD = (split /{/, $Record54)[0];
  $RECORDxRI = $RECORD . ',' . $Record38; 

  build_list( $RECORD, $RI, $RECORDxRI, \%$RECORDxRI_count, \%EACH_REC
+ORD );
}
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• I explicitly named the "global" variables, just for ease-of-maintenance.
• $RI was always unused in build_list — I left it here because I suppose you are doing more than the posted code shows.
• You had @ instead of $ when getting indices from @record. If you only want one value, don't use a slice.
• I almost just defined the "global" hashes as references in the first place (to avoid the backslashes altogether).
  Update: See btrott's answer for more on this.
  Like:
  my $RECORDxRI_count = {};
  my $EACH_RECORD     = {};

Hope this is helpful...
Russ