Well, I think OpenSSL has documented this pretty well:
If an alternative RAND_METHOD implementation is being used (either set
directly or as provided by an ENGINE module), then it is entirely
responsible for the generation and management of a cryptographically
secure PRNG stream. The mechanisms described below relate solely to
the software PRNG implementation built in to OpenSSL and used by
These functions implement a cryptographically secure pseudo-random
number generator (PRNG). It is used by other library functions for
example to generate random keys, and applications can use it when they
The RAND_SSLeay() method implements a PRNG based on a cryptographic hash function.
hash function; currently SHA-1
So that is certainly not Dual_EC_DRBG. You can switch RNG method by using
RAND_set_rand_method but setting a different ENGINE should be preferred for newer applications.
Note that it would not hurt to check this in the source of the openssl implementation you are using. I don't believe it has changed yet, but openssl documentation is not known for its, eh, "up to dateness".