Try using this:

use strict;
use warnings;
use Data::Dumper;

my $string="((mouse,rat),(human,chimp))";
my $tree=[];

die "Invalid char in input string" if $string !~ /^[(),\w]+$/;
my @tokens=$string=~/(\(|\)|,|\w+)/g;
my @stack=($tree);

foreach (@tokens) {
  if ($_ eq '(') {
    my $new=[];
    push(@{$stack[@stack-1]},$new);
    push(@stack,$new);
  } elsif ($_ eq ')') {
    die "Mismatched ')'" if @stack < 2;
    pop(@stack);
  } elsif ($_ ne ',') {
    push(@{$stack[@stack-1]},$_);
  }
}
die "Mismatched '('" if @stack != 1;

$tree=$tree->[0];

print Dumper($tree);
[download]

Updated: added validity check on input string.