CE certification is not a single certificate, but a collective term for a set of EU product regulations. A product is only compliant when it simultaneously meets all applicable directives (such as LVD, EMC, RED, RoHS), completes testing, establishes technical documentation, has the manufacturer sign a Declaration of Conformity (DoC), and bears the CE mark. Only products that require the involvement of a Notified Body (NB) will receive an EU-type examination certificate issued by the NB.
The legal meaning of the CE mark is "the manufacturer declares that the product complies with applicable EU regulations," and the responsibility lies with the manufacturer, not with any issuing body. This is also why most documents marketed as "CE certificates" are actually attestations self-issued by third parties and have limited legal effect—what is truly valid is the technical documentation + DoC.