while (<DATA>) {
    if (/^[CETLMNPA](?:,[CETLMNPA])*$/) {
        print "Validated: $_";
    } else {
        print "Incorrect: $_";
    }
}

__DATA__
C,M,N
C,MN
C,,M,N
P
T
Z
E,M,N,P,A,A
[download]

my @list = split m/,/, $CD;

Then your processing might be easier...

if $CD =~ /[CETLMNPA,]+/ {
 print "it matched\n";
 }
[download]

This is not working. When $CD ="CM" (which is invalid) It says it matched. The letters must be seperated by comma (,)
valid values are: "C,M" "C" "C,P"
invalid values are : "CM", "PC" (each letter must be seperated by comma(,))

I'm not sure from your question what exactly you're trying to accomplish. Here are a couple of options...

1. Determine if the value in $CD is valid

   my $valid_chars = 'CETLMNPA';
   if ($CD =~ m/^[$valid_chars](?:,[$valid_chars])*$/) {
      print "Valid!"
   }
   else {
      die "Invalid!"
   }
   [download]

   Let's break down that regular expression:

   m/
      ^[$valid_chars]   #the string must start with one of the valid char
   +s
      (?:               #start group, but don't capture!
         ,              #could have a comma
         [$valid_chars] #and another valid char
      )*                #and that comma+valid char could repeat 0 or more
   + times
      $                 #until the end of the string
   /x                   #this is here to allow me to use all these commen
   +ts
   [download]

2. Use as configuration values

   For example, if I want to know at various points in code if a given flag is set:

   my %config = map { $_ => 1 } split(',', $CD);
   ## later on...
   if ( $config{L} ) { print "L was set!" }
   [download]

   You might use the validation from above in combination with this.