Ce marking design rules
You have to provide a Declaration of Conformity when importing, and the product must have the CE logo.

With it you declare your design is safe an follows the required regulations.
Eg: does not contain banned materials, is not a fire hazard, safe for humans or has warning signs, does not disturb the operation of other devices with unwanted emitted or conducted interference, does not become unsafe when disturbed by interference. 

So many guidelines and regulations that only the very large companies can afford to check and test them all. But you can ask experts for an opinion, or ask a test site to perform EMI emission and immunity tests. Which are the most important.
After all, you don't want to disturb cellular, gps or walkie-talkies.

There is no governing body apart from customs who should prevent importing of non-CE goods. However, if your product caused problems or harm you might be investigated, and possibly taken to court by a public prosecutor.