I'm going on the assumption that you don't want the keys to be assigned to a list, but rather you want the hash values for a particular month to be assigned to the list. I haven't bothered sorting the result as you can sort the list however you want once it is assigned.

#!/usr/bin/perl
use warnings;
use strict;

my %ManagerInCharge = ( 
200610 => { 
1 => "jane", 
2 => "john", 
3 => "joe", 
4 => "frank", 
}, 

200701 => { 
1 => "gunder", 
2 => "abel", 
3 => "frank", 
}, );

my $month = "200701";
#
# If you need the keys assigned, then the statement
# my @slice = keys %{$ManagerInCharge{$month}} 
# is enough.
#
my @slice = map { $ManagerInCharge{$month}{$_} } 
                ( keys %{$ManagerInCharge{$month}} );
for (@slice) {
   print "value is $_\n";
}
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and the results are:

C:\Code>perl assign_slice.pl
value is gunder
value is frank
value is abel
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