You may try removing extreme units (best and worst) and then performing a non-parametric rank test (Sperman)

There are two directions of analyzing the sensitivity of DEA efficiency scores :

1. Sensitivity analysis of model changes  : basically you are trying to assess if using different input and output variables changes the DMUs' efficiency classification. This exercise basically allows you to see what effect of different input/output variables have on the DEA results. I think this analysis is heavily driven by the theory of production specific to each industry. You do not require any specific software to do this.

2. Sensitivity analysis of data variation : This form of analysis assess what effect would you see if the sample/population of the DMUs change. Since DEA is a non-parametric approach and unable to separate data noise from signal, any outlier and data errors will cause the DMUs to be reclassified (as efficient/inefficient). The common way of doing so will be to manually test for excluding outliears from the sample or doing some bootstrapping DEA. I use R to do this. Two packages in R is good for this : Benchmarking and FEAR packages. They have their respective strength and weaknesses