First off: check whart sort of format you exported from your browser. You'll want PEM (plain base64 text with a -----BEGIN CERTIFICATE----- line at start). Try opening your file in a text editor and check if that's what you have. Export in different formats or convert your current file to PEM format (see the OpenSSL manual for that or the openssl) man page on a Unix system.
In short: when using HTTPS_CA_DIR you need a directory with PEM certificates in files named according to the hash of their (certificate) subject name. Perhaps HTTPS_CA_FILE is more useful for you (if you only have a single CA certificate to handle).
Why? The CA file directory should hold files in so-called PEM format and follow the instructions as listed in Crypt::SSLeay under Client Certificate Support. In fact, that points to the OpenSSL docs again with more instructions.