Some thoughts:

1. prepare_cached() the initial query
2. Loop over the initial query. (Using IN instead of = ...)
3. Use an array slice in the second execute() statement. (@assign[0..11] instead of $assign[0], $assign[1], etc.)

Essentially, it would boil down to this:

my @audit_params = keys %$audits;
my $audit_params_string = join ',', ('?') x @audit_params;
my $audit_sql = <<__END_SQL__;
SELECT AuditID, Referrals.1, Referrals.2, Referrals.3,
                              Referrals.4, Referrals.5,
                              Referrals.6, Referrals.7, Referrals.8,
                              Referrals.9, Referrals.10, 
                              Referrals.11, Referrals.12,
                              Referrals.13, Referrals.14, States.1
                         FROM   Referrals
                         INNER JOIN States On (Referrals.10 = States.1
+)
                         WHERE AuditID IN ($audit_params_string)
__END_SQL__

my $audit_sth = $dbh->prepare_cached($audit_sql) || die "Cannot prepar
+e() '$audit_sql'\n";
$audit_sth->execute(@audit_params) || die "Cannot execute() '$audit_sq
+l' with '@audit_params'\n";

my $insert_sql = <<__END_SQL__;
INSERT INTO report_printing_table
                          (1,2,3,4,5,6,7,8,9,10,11,12,13)
                       VALUES (?,?,?,?,?,?,?,?,?,?,?,?,?)
__END_SQL__

while (my @assign = $audit_sth->fetchrow_array)
{
    my $audit_id = shift @assign;
    my $insert_sth = $dbh->prepare_cached($insert_sql) || die "Cannot 
+prepare() '$insert_sql'\n";
    $insert_sth->execute($audit_id, @assign[0..11]) || die "Cannot exe
+cute '$insert_sql' with '$audit @assign[0..11]'\n";
    $insert_sth->finish;
}

$audit_sth->finish;
[download]

FYI: Code is completely untested.

------
We are the carpenters and bricklayers of the Information Age.

The idea is a little like C++ templates, except not quite so brain-meltingly complicated. -- TheDamian, Exegesis 6

Please remember that I'm crufty and crochety. All opinions are purely mine and all code is untested, unless otherwise specified.