Apparatus and method for processing specimens, e.g., biological specimens, to extract samples for both liquid (i.e., extracellular) and slide-based (i.e., intracellular) testing. Both types of samples can be obtained from a single fluid specimen. A fluid sampling station removes fluid from a specimen container and places it in a sample receptacle. A specimen acquisition station removes fluid from the container, separates particulate matter (e.g., cells) from the removed fluid, and forms a sample layer of particulate matter, which is transferred to a slide. The two sampling operations can be carried out in any order. The fluid sample receptacle may have a special one-way valve arrangement. The apparatus can be automated so as to process multiple fluid specimens in their respective containers. The machine according to this invention is a "platform instrument" that can produce all required liquid samples and slide-based samples for essentially all cytopathology tests.