Hey,
maybe you can find some additional information on this in the PHP logfiles or a configuration in curl to make the message more verbose? From what i know curl is a PHP module which is used by ownCloud so additional logging could be end up there.
It seems additional information are also available in the curl manual:
CURLE_SSL_CONNECT_ERROR (35)
A problem occurred somewhere in the SSL/TLS handshake. You really want the error buffer and read the message there as it pinpoints the problem slightly more. Could be certificates (file formats, paths, permissions), passwords, and others.
which i had found here: libcurl - Error Codes
Sure, i think this is fully understandable. But if i’m searching here in the forums for this curl 35 error:
https://central.owncloud.org/search?q=%22curl%22%20%22error%2035%22
i’m finding many people already trying this without much success. Sometimes one needs to go a different way if the initial issue can’t be solved. 
Additionally i have read from so many problems about the updater app in the past (e.g. Update to 10.1.0 not offered from 10.0.10.4 · Issue #34625 · owncloud/core · GitHub is the most recent where an update from 10.0.10 to 10.1.0 isn’t offered ).
Because of such recurring issues i personally wouldn’t spend much time into fixing issues with that updater app and chose the more reliable (but maybe a little bit more time consuming) alternative to update manually.