The CRL storage service stores CRLs. The service takes a CRL-storage request (see Section 3.3) specifying the CRLs to be stored, stores the CRLs, and returns a CRL-storage reply (see Section 3.4) acknowledging the request.
The certification authority stores a CRL only if its signature and certification path are valid, following concepts in RFC 1422 (Although a certification path is not required in a CRL-storage request, it may help the certification authority validate the CRL.)