std::string in C#?

std::string and c# string are not compatible with each other. As far as I know the c# string corresponds to passing char* or wchar_t* in c++ as far as interop is concerned.
One of the reasons for this is that There can be many different implementations to std::string and c# can't assume that you're using any particular one.

Try something like this:

bool __declspec( dllexport ) OpenA(const TCHAR* pFile)
{ 
   std::string filename(pFile);
   ...
   return true;
}

You should also specify the appropriate character set (unicode/ansi) in your DllImport attribute.

As an aside, unrelated to your marshalling problem, one would normally pass a std:string as a const reference: const std:string& filename.