I did, so I looked it up.  The short form is that whoever supplied a section owns it and their laws apply to the goin’s on in that section.

The Intergovernmental Agreement allows the Space Station Partners States to extend their national jurisdiction in outer space, so the elements they provide (e.g. laboratories) are assimilated to the territories of the Partners States.

“The basic rule is that ‘each partner shall retain jurisdiction and control over the elements it registers and over personnel in or on the Space Station who are its nationals’ (Article 5 of the Intergovernmental Agreement).

“This means that the owners of the Space Station – the United States, Russia, the European Partner, Japan and Canada – are legally responsible for the respective elements they provide. The European States are being treated as one homogenous entity, called the European Partner on the Space Station. But any of the European States may extend their respective national laws and regulations to the European elements, equipment and personnel.

“This extension of national jurisdiction determines what laws are applicable for activities occurring on a Partner’s Space Station elements (e.g. European law in the European Columbus Laboratory). This legal regime recognises the jurisdiction of the Partner States’s courts and allows the application of national laws in such areas as criminal matters, liability issues, and protection of intellectual property rights. Any conflicts of jurisdiction between the Partners may be resolved through the application of other rules and procedures already developed nationally and internationally.”

http://www.esa.int/Our_Activities/Human_Spaceflight/International_Space_Station/International_Space_Station_legal_framework