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Analysis of genetic and functional variability in populations of living cells requires experimental techniques capable of monitoring cellular processes such as cell signaling of many single cells in parallel while offering the possibility to sort interesting cell phenotypes for further investigations. Although flow cytometry is able to sequentially probe and sort thousands of cells per second, dynamic processes cannot be experimentally accessed on single cells due to the sub-second sampling time. Cellular dynamics can be measured by image cytometry of surface-immobilized cells, however, cell sorting is complicated under these conditions due to cell attachment. We here developed a cytometric tool based on refractive multiple optical tweezers combined with microfluidics and optical microscopy. We demonstrate contact-free immobilization of more than 200 yeast cells into a high-density array of optical traps in a microfluidic chip. The cell array could be moved to specific locations of the chip enabling us to expose in a controlled manner the cells to reagents and to analyze the responses of individual cells in a highly parallel format using fluorescence microscopy. We further established a method to sort single cells within the microfluidic device using an additional steerable optical trap. Ratiometric fluorescence imaging of intracellular pH of trapped yeast cells allowed us on the one hand to measure the effect of the trapping laser on the cells' viability and on the other hand to probe the dynamic response of the cells upon glucose sensing.