You would be better off making your own widget on a sub-classed Canvas. However you could bind a right mouse button click to each checkbutton, to simulate 3 states.

#!/usr/bin/perl
use warnings;
use strict;
use Tk;
use Tk::Pane;

my @states = qw(Alaska Hawaii Michigan Georgia Arizona Washington Oreg
+on California Texas Utah Minnesota);

my $mw = tkinit();
$mw->geometry('300x300+100+100');

my $sp = $mw->Scrolled('Pane', -scrollbars=>'osoe', sticky=>'nwse')
     ->pack(-expand=>1, -fill=>'both' );

my %cbs;
my @cbvalues;
my @cbnames;
my $count = 0;

foreach my $d( @states){

  $cbnames[$count] = $d;

  $cbs{$count} = $sp->Checkbutton(-text => $d,
        -font=>[arial => 12],
        -onvalue => 1,
        -offvalue => 0,
        -variable => \$cbvalues[$count],
        -font => 'big',
        -bg => 'white',
     )->pack(-anchor=>'w')->pack();

  $cbs{$count}->bind('<ButtonRelease-3>', sub{  
                              print "@_\n";
                              print "do you 3rd state thing here\n"; 
                             });


$count++;
}

my $showbutton= $mw->Button(-text=>'Show Selected',
-bg => 'lightyellow',
-command => sub{ 
       my @selected = ();
       foreach my $c( 0.. $count ){
            if ( $cbvalues[$c] ){
                push @selected, $cbnames[$c];
              }
         }
  
      print "@selected\n"; 
      } )->pack();

MainLoop();
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