Like haukex I wouldn't use such a low-level module by default. Here is an example using LWP::UserAgent and a known, public endpoint. Perhaps you can start from here and then modify to your needs?

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

use LWP::UserAgent;
use Data::Dumper;

my $url      = 'https://server.cryptomix.com/secure/';
my $keyfile  = 'foo.key';
my $certfile = 'foo.cert';
my $ua = LWP::UserAgent->new (
    ssl_opts => {
        SSL_cert_file => $certfile,
        SSL_key_file  => $keyfile
    }
);

my $res = $ua->get ($url);
print $res->status_line;
print $res->decoded_content;
[download]

This assumes that you have the RSA key in foo.key and the PEM client cert in foo.cert. You'll get lots of info back from that server.