<p>In C# there is a method <code>SetApartmentState</code> in the class <code>Thread</code>.
How do I do the same thing in C++?</p>

c++ doesn't have built in thread support. What you are looking for depends on how you are implementing threads in your application. Win32? pthreads? boost::threads? Whichever API you are using will determine the answer to your question.
EDIT: looks like this may have an example for you:
http://msdn.microsoft.com/en-us/library/system.threading.apartmentstate.aspx
It looks like it applies to managed c++.