LDAP configuration with TLS Key

I'm trying to connect an owncloud instance to a LDAP server. My admins have an "interesting" configuration. A connection ist done unencrypted but STARTTLS (ldapsearch -Z) is required. SASL is not used (ldapsearch -x). The method for authentication is a TLS key. My ~/.ldaprc looks like this:

TLS_REQCERT     demand
TLS_CACERT      /path/to/CA.pem
TLS_CERT        /path/to/local.pem
TLS_KEY         /path/to/local-key.pem

The ldapsearch tool must be called like this to work:

ldapsearch -x -Z

Can anyone explain, how to configure an owncloud server to be compatible with this LDAP setup?

Server configuration
Operating system: Debian 8
Web server: Apache 2.4.10
Database: MySQL 5.5
PHP version: 5.6.27
ownCloud version (see ownCloud admin page): 9.1.1 (stable)
Updated from an older ownCloud or fresh install: fresh
Special configuration (external storage, external authentication, reverse proxy, server-side-encryption): none

Integrity status for oC9+

No errors have been found.