Your module doesn't even compile. How could it have given that output?

Below, I

• BUG: Changed mship::stat->(...) to mship::stat(...). (This is the answer to your question.)
• BUG: Moved package mship;. croak was being imported into the wrong namespace.
• BUG: Added missing my in stat.
• BUG: Removed the croaks after the returns. return never fails, so the croaks would never be reached.
• Renamed stat to accepts_conn to avoid confusion with the builtin function stat.
• Changed to require "mship.pm"; to use mship;
• Returned a better result from accepts_conn (formerly stat). (Save the conversion to strings for when it's time to print. Work with true and false until then.)
• Uppercase variable names are usually constants. Changed the case of connection's arguments.
• Simplified $port_name = A or $port_name = B; to $port_name = A or B;.
• Added spacing so I could see what I was doing.
• Is confused as to the purpose of connection.

use strict;

package mship;

use IO::Socket::INET;
use Socket;
use Carp;


##############
sub connection
##############
{
    my ( $ip, $tcp_port ) = @_;


    my $ipadd       = Socket::inet_aton($IP) or
                         croak "$IP is not valid\n";

    my $port_name   = getservbyport($TCP_PORT, 'tcp') or "unknown";

    my $remote_name = gethostbyaddr( $ipadd, 2 ) or
                         croak "Unable to resolve hostname for $IP\n";

    my %stats = (
        'ip'          => $ip,
        'port'        => $tcp_port,
        'port_name'   => $port_name,
        'remote_name' => $remote_name,
        'status'      => accepts_conn($IP, $TCP_PORT) ? "Up" : "Down"
    );

    print "sub connection port = $TCP_PORT IP = $IP\n";
    return %stats;
}


#############
sub accepts_conn
#############
{
    my ( $ip, $tcp_port ) = @_;

    my $sock = IO::Socket::INET ->new(
        Timeout  => 5,
        PeerAddr => $ip,
        PeerPort => $tcp_port,
        Proto    => 'tcp',
    );

    return $sock ? 1 : 0;
}


1;
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#!/usr/bin/perl -w
use strict;

use mship;


my %stats = mship::connection('xxx.19.208.27', '9101');

while (my ($key, $value) = each(%stats))
{
    print "$key = $value\n";
}


print "\n";


my $status = mship::accepts_conn('xxx.19.208.27', '9101') ? "Up" : "Do
+wn";
print("Status: $status\n");
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