#!/usr/bin/perl -w
use strict;

my $string="CCCAAAAACCCAAAAAAACCCCBBBCCAAACCBBACBBAAAAAAAAAAACAAAAAAAA
+AA";

my $nA = $string =~ tr/A//;
my $nB = $string =~ tr/B//;
my $nC = $string =~ tr/C//;

print "A=$nA B=$nB C=$nC"; #A=37 B=7 C=16

#compare these 3 as you will to handle cases like 
#all are the same, etc
[download]

What have you tried? We generally appreciate a show-of-effort here - see How do I post a question effectively?.

There is no way to determine the most frequent letter without counting and comparing, and brevity of source code is generally not a good goal in and of itself (unless you are golfing).

That said, one way (TIMTOWTDI) to accomplish the counting with very little code is using inline Foreach Loops and split with a hash. You can then use sort with the numerical comparison operator (<=>) to find the key with the maximum value:

my $my_string="CCCAAAAACCCAAAAAAACCCCBBBCCAAACCBBACBBAAAAAAAAAAACAAAAA
+AAAAA";
my %count;
$count{$_}++ foreach split //, $my_string;
print Dumper \%count;
print my ($most_common) = sort {$count{$b} <=> $count{$a}} keys %count
+;
[download]

Modified to handle cases with several characters with the maximal number of occurences:

  my %count;
  $count{$_}++ foreach split //,$string;
  my $max = (sort {$a<=>$b} values %count)[-1];
  print $max,' ',grep $count{$_} == $max,keys %count;
[download]

use List::Util 'reduce';
use 5.010;
my %hash;
$hash{$_}++ for split //, $my_string;
say "Most frequent: ", reduce {$hash{$a} > $hash{$b} ? $a : $b} keys %
+hash;
[download]

If there are several characters with most occurences, this code will report just one of them.

this code will report just one of them

Indeed. As specified. Notice the title: ...find the letter.... It did not say ...find the letters....

You have to count, unless you're OK with an approximation.

It's short, runs in constant time, and is right 1/3 of the time. :-)