Why don't you just always treat them as references? Then you won't have to reference/dereference them each time.

# Define them as hash references.
my $RECORDxRI_count_REF = {};
my $EACH_RECORD_REF = {};

while (<DATA>) {
    ....
    # Call build list--now you don't need to
    # take references to the hashes, because they're
    # already references
    build_list( $RECORD, $RI, $RECORDxRI, $RECORDxRI_count_REF, $EACH_
+RECORD_REF );
    ....
}

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

    # These are hash references. To access them,
    # you *don't* need to assign them to hashes.
    # Just use the -> operator, which automatically
    # dereferences them.
    $RECORDxRI_count->{$RECORDxRI}++;
    $EACH_RECORD->{$RECORD} = '';
}
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Read perlref if this doesn't make sense.