Legal obligations when designing electronics
Concerning the EU market, this is the main site that lists the regulation directives. 

Given the product type and the typical usage of your product, you have to dig into all this regulations and check the applicable standards listed on that site.

Hint: Find a CE declaration of conformity for an existing product that is similar to your product. The declaration will contain the applicable standards. (Every product on the EU marked must have a CE DoC publicly available).