I'm also encountering this issue on an Ubuntu 14.04 based machine - version details for curl are:

$ curl -v "https://intouch.techdata.com/"
* Hostname was NOT found in DNS cache
* Trying 80.152.49.70...
* Connected to intouch.techdata.com (80.152.49.70) port 443 (#0)
* successfully set certificate verify locations:
* CAfile: none
  CApath: /etc/ssl/certs
* SSLv3, TLS handshake, Client hello (1):
* Unknown SSL protocol error in connection to intouch.techdata.com:443
* Closing connection 0
curl: (35) Unknown SSL protocol error in connection to intouch.techdata.com:443

$ curl -V
curl 7.35.0 (x86_64-pc-linux-gnu) libcurl/7.35.0 OpenSSL/1.0.1f zlib/1.2.8 libidn/1.28 librtmp/2.3
Protocols: dict file ftp ftps gopher http https imap imaps ldap ldaps pop3 pop3s rtmp rtsp smtp smtps telnet tftp
Features: AsynchDNS GSS-Negotiate IDN IPv6 Largefile NTLM NTLM_WB SSL libz TLS-SRP

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** [bugs:#1376] https not working for specific domains**
**Status:** closed-works-for-me
**Labels:** https 
**Created:** Fri May 30, 2014 01:15 PM UTC by Altruista
**Last Updated:** Sun Jun 15, 2014 09:24 PM UTC
**Owner:** Daniel Stenberg
https doesn't work with specific domains. tested on 7.35, 7.36 and 7.37 on ubuntu 14.04
try this URL https://intouch.techdata.com/
    > curl --verbose "https://intouch.techdata.com/"
    * Hostname was NOT found in DNS cache
    *   Trying 80.152.49.70...
    * Connected to intouch.techdata.com (80.152.49.70) port 443 (#0)
    * successfully set certificate verify locations:
    *   CAfile: /etc/ssl/certs/ca-certificates.crt
      CApath: none
    * SSLv3, TLS handshake, Client hello (1):
    * Unknown SSL protocol error in connection to intouch.techdata.com:443 
    * Closing connection 0
    curl: (35) Unknown SSL protocol error in connection to intouch.techdata.com:443 
i used few online SSL tools, SSL for this domain seems to be configured OK. site works in browsers etc.
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