You may get encounter error “CHECK_NRPE: Error - Could not complete SSL handshake” from Nagios monitoring you need to check  SSL or nrpe file configuration

Current Status:  CRITICAL  (for 0d 0h 1m 32s)
Status Information: CHECK_NRPE: Error - Could not complete SSL handshake.

1. Be ensure openssl-devel package be installed in your system. If it’s not, install that using YUM command

2. Check the nrpe configure file make sure the only_from = is the IP of Nagios monitoring server.
 
[root@host]#   yum install  openssl-devel

[root@host]#  vi /etc/xinetd.d/nrpe
 
service nrpe
{
        flags           = REUSE
        socket_type     = stream
        port            = 5666
        wait            = no
        user            = nagios
        group           = nagios
        server          = /usr/local/nagios/bin/nrpe
        server_args     = -c /usr/local/nagios/etc/nrpe.cfg --inetd
        log_on_failure  += USERID
        disable         = no
        only_from       = 127.0.0.1 192.168.0.1
}

Assume that  the nagios server  IP address is 192.168.0.1 and Client IP Address : 192.168.0.10

also check in your nrpe.cfg file Nagios server IP address added on allowed_hosts.
 
[root@host]# vi /usr/local/nagios/etc/nrpe.cfg

allowed_hosts=127.0.0.1  192.168.0.1

Now, restart xinetd,
 
root@host2 [~]# /etc/init.d/xinetd restart
Stopping xinetd:                                           [  OK  ]
Starting xinetd:                                             [  OK  ]

[root@localhost ~]# /usr/local/nagios/libexec/check_nrpe -H 192.168.0.10
NRPE  v2.12

I hope, after you did will never facing this issue on Nagios Monistroing.