EE checks against CRL for all certificate types

EEs also check all relevant certificates, i.e., certificates of received messages that are processed, against the CRL. This includes OBE pseudonym, OBE identification, and RSE application certificates. It is up to EE whether it checks non-relevant certificates, i.e. certificates or received messages that are not processed, against the CRL.

These checks are specified in IEEE 1609.2.
Clause 5.1.3.4 describes how an EE checks whether a pseudonym certificate has been revoked by calculating the linkage values from the linkage seeds listed in the CRL, and comparing the calculated linkage value against the linkage value in the inspected certificate. Clause 6.4.10 and 6.4.11 contain additional information about linkage values.
Clause 5.1.3.5 describes how an EE checks whether an OBE identification and RSE application certificate has been revoked by calculating the hash value of the inspected certificate, and comparing it against a CRL entry.
Clause 7 contains comprehensive information about CRLs.

This is out of scope since it defines EE's behavior.