Since Android 4.2, Android's TLS implementation supports TLS v1.1 and TLS v1.2, but it's not enabled by default. So, it's not enabled in okhttp, too (because it just takes the SSLSocketFactory from SSLContext.getInstance('TLS')).
I have played around with ConnectionSpec, but as I have understood it, ConnectionSpec is to set the allowed TLS versions, ciphers etc. and not to manipulate the enabled protocols of SSL sockets – please correct me if I'm wrong.
For Android 5.0+, TLSv1.1/1.2 is used when possible as expected.
Maybe you'll consider enabling TLS v1.1 and TLS v1.2 for Android >= 4.2 < 5.0 too. You can find some details in my blog article: http://blog.dev001.net/post/67082904181/android-using-sni-and-tlsv12-with-apache. My current workaround is to use a compatibility socket factory.
If you know an easier solution to get TLSv1.1/1.2 on Android <5 with okhttp, please let me know.
See also http://stackoverflow.com/a/29252730