For the European market you need to CE mark all electronics. In this case by providing a Declaration of Conformity (DoC) to the EMC Directive. And in case of 230VAC supply etc, also the LVD directive. The DoC in turn is a legally binding document where your company states that, yes, we follow these directive(s). You also need a physical CE mark on the product "if feasible".
The directives in turn point to standards that can be used to fulfil the directive, but that's another story.
You probably don't have to perform a 3rd party verification by a test house however. But in case your product happens to have poor EMC performance out in the field, you'll be in for some major trouble if you can't prove that you've taken all necessary precautions.
If an approved test house has said that your product is fine, then you have your back free in court. As in: we have tried our best to ensure that this product is compliant. But you can of course still be forced to withdraw the product from the market etc.