Many hospital rankings are based on algorithms and weights elicited by experts. The paper attempts to build rankings of Polish district hospitals using the TOPSIS method and to examine the sensitivity of the results to the changes in weights. We considered 11 large and 34 medium-sized hospitals. The criteria set consists of man-days total, profit/loss on sales, contract with the National Health Fund, return on assets (ROA) and return on equity (ROE). Because of this, rankings take into account different spheres in which hospitals perform, including the financial aspect and their main goal, i.e. treating patients. The results show that despite the overall high similarity of rankings, the benchmarking based on rankings should be done with care as the positions of some individual hospitals changed to a great degree.