Depends on the nature of your product that you intend to CE-Mark. Here are some brief examples where testing is required:
1. Your product includes electronics that could generate RF. You would have to undergo EMC testing to assure that your product does not exceed maximum allowable emissions. You would include the test lab's report in your technical dossier.
2. You are building an enclosure in which you intend to house electronics for use in Ex Zone 2. You must test the enclosure to demonstrate that it meets the required IP rating. The results would be in your test report.
If your product cannot be shown to comply with applicable EU directives by calculations, tables, or exemptions, then you must perform tests to prove compliance.
By the way, CE is not a certification. It's a declaration of conformity, declaring that the product complies with all EU directives applicable to the product. With the CE-Mark, a product can be sold throughout the EU and be transported across borders within the EU. The certification is different. A product usually has to meet multiple certifications. Many of these may be self certified. The ones that address the most hazardous conditions must be performed by a Notified Body, such as TUV, BV, DNV, etc.
When you get your technical dossier together, it must be lodged (stored) within the EU member states. Often a Notified Body will offer this service for a small fee. If the Notified Body lodging the dossier had no hand in assembling these documents, they will treat what you give them simply as an envelope or CD, without regard to the validity of the content.
A final word about CE-Mark. If you put it on a product but the product knowingly doesn't comply, you could be exposed to criminal charges in the EU.
I touched on just a few high points; there's far more to this. I encourage you to work with a Notified Body if this is your first time through this process!