Here's another option:

use Modern::Perl;
use Data::Dumper;

my @array;
my $str =
  "1. ...... AB_CD 1.1 ...... EF_GH 1.2 .... IJ_KL_MN 2. ............ 
+OPQR";

while ( $str =~ /(\d+\.\d*)\s+\.+\s+(\S+)\s*/g ) {
    push @array, { chapter => $1, name => $2 };
}

say Dumper \@array;
[download]

Output:

$VAR1 = [
          {
            'name' => 'AB_CD',
            'chapter' => '1.'
          },
          {
            'name' => 'EF_GH',
            'chapter' => '1.1'
          },
          {
            'name' => 'IJ_KL_MN',
            'chapter' => '1.2'
          },
          {
            'name' => 'OPQR',
            'chapter' => '2.'
          }
        ];
[download]

The regex:

/(\d+\.\d*)\s+\.+\s+(\S+)\s*/g
   ^  ^ ^   ^  ^  ^   ^   ^  ^
   |  | |   |  |  |   |   |  |
   |  | |   |  |  |   |   |  + - Globally
   |  | |   |  |  |   |   + - 0+ spaces
   |  | |   |  |  |   + - Capture non-whitespace characters
   |  | |   |  |  + - 1+ spaces
   |  | |   |  + - Multiple periods
   |  | |   + - 1+ spaces
   |  | + - Capture zero or more digits
   |  + - Capture a period
   + - Capture one or more digits
[download]

Hope this helps!