I found the way to check.
After i perform the transaction with multi stack.

long authType;
curl_easy_getinfo(easyHandle, CURLINFO_PROXYAUTH_AVAIL, &authType);
// 0 - no authentication was performed
// 8 - NTLM
// 1 - Basic

I have checked it and it looks working.
It return 0 if no authentication was requested by the proxy and other value if one of auhtentication types was requested.