If your product does not fall within the scope of harmonization regulations according to 1., then the CE marking is prohibited.
All products subject to at least one of the harmonisation regulations (EU directive or regulation) may only be placed on the market with CE marking.
The CE marking is legally binding in all member states of the European Economic Area and Turkey. The European Economic Area includes the member states of the European Union (EU) and the member states of the European Free Trade Area (EFTA).
The CE marking is of course necessary for products that you sell publicly and offer on the market (put on the market). However, this also applies if your product is only used for personal use [4]
Therefore, distributors can not choose whether they want the product CE marking or not, but either CE marking is required by product safety law in conjunction with one or more EU directives or if it is not mandatory, it is automatically banned [1].
[1] Wolfram Pichler, EU Conformity Assessment in archt project phases directly to the goal, The recipe book for designers, product managers and CE coordinators, 2018
[2] Hans-Joachim Hess & Tom Gördes, product liability in Germany and Europe, the practical handbook for entrepreneurs and executives - with case studies, samples and checklists, second new edited edition, 2019
[3] Michael Loerzer, Peter Buck, Andreas Schwabedissen, Legally compliant marketing of products. In 10 steps to the declaration of conformity, 2nd updated and extended edition, Beuth
[4] Jörg Ertelt, basic knowledge CE marking, CE marking in Europea and the rest of the world: Who does the CE marking concern?
[5] Wikipedia, European Economic Area, Aug. 2020, https://de.wikipedia.org/wiki/Europ%C3%A4ischer_Wirtschaftsraum