You should use the soft_close() or hard_close() methods. Please take a look at the documentation for the Expect module. Here's a simple example:

#!/usr/bin/perl

use strict;
use warnings;
use Expect;

my $command = "cat > tmp.txt";
my @params;
my $exp = Expect->spawn($command, @params)
    or die "Cannot spawn $command: $!\n";

print("sending...\n");
$exp->send("Hello world\n");
sleep 1;
$exp->hard_close;

__END__
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Or, if you really want to send Ctrl-C to your process, try this: $exp->send("\cC");. Or you can just send a signal to the process like Fletch recommends.