The journey of sperm navigation towards ovum is one of the most important questions in mammalian fertilisation and reproduction. However, we know very little about spermatozoa propagation in a complex fluidic, chemical and topographic environment of a fertility tract. Using microfluidics techniques, we investigate the influence of cell-cell interactions on spermatozoa swimming behavior in constrained environment at different concentrations. Our study shows that at high enough cell concentration the interaction between boundary-following cells leads to formation of areas with preferential direction of cell swimming. In the microchannel of a rectangular cross-section, this leads to formation of a "four-lane" swimming pattern with the asymmetry of the cell distribution of up to 40%. We propose that this is caused by the combination of cell-cell collisions in the corners of the microchannel and the existence of morphologically different spermatozoa: slightly asymmetric cells with trajectories curved left and the symmetric ones, with trajectories curved right. Our findings suggest that cell-cell interactions in highly folded environment of mammalian reproductive tract are important for spermatozoa swimming behavior and play role in selection of highly motile cells.