John-Mark Bell filed bug #3000052 that identified a problem (with
an associated patch) with the OpenSSL handshake state machine
when the multi interface is used:

Performing an https request using a curl multi handle and using
select or epoll to wait for events results in a hang. It appears
that the cause is the fix for bug #2958179, which makes
ossl_connect_common unconditionally return from the step 2 loop
when fetching from a multi handle.

When ossl_connect_step2 has completed, it updates
connssl->connecting_state to ssl_connect_3. ossl_connect_common
will then return to the caller, as a multi handle is in
use. Eventually, the client code will call curl_multi_fdset to
obtain an updated fdset to select or epoll on. For https
requests, curl_multi_fdset will cause https_getsock to be called.
https_getsock will only return a socket handle if the
connecting_state is ssl_connect_2_reading or
ssl_connect_2_writing.  Therefore, the client will never obtain a
valid fdset, and thus not drive the multi handle, resulting in a
hang.

(http://curl.haxx.se/bug/view.cgi?id=3000052)