The manufacturer might be responsible however if they are not in the EU they must appoint a EU based authorised representative in most situations that is an importer or distributor. The words ‘place on the market’ also have special legal significance and it might be the manufacturer who does it or it might be the importer.It's been a while since I went through the process but IIRC the manufacturer is responsible for the CE mark and supporting paperwork, no matter where the product is made. As long as the importer has paperwork from the manufacturer supporting compliance no additional testing is needed.