High-throughput cell sorting with flow cytometers is an important tool in modern clinical cell studies. Most cytometers use biomarkers that selectively bind to the cell, but induce significant changes in morphology and inner cell processes leading sometimes to its death. This makes label-based cell sorting schemes unsuitable for further investigation. We propose a label-free technique that uses a digital inline holographic microscopy for cell imaging and an integrated, optical neural network for high-speed classification. The perspective of dense integration makes it attractive to ultrafast, large-scale cell sorting. Network simulations for a ternary classification task (monocytes/granulocytes/lymphocytes) resulted in 89% accuracy