Inference can again be based on a conditional permutation approach. This consists of holding the tuple of values observed at i fixed, and computing the statistic for a number of permutations of the remaining tuples over the other locations. Note that because the full tuple is being used in the permutation, the internal correlation of the variables is controlled for, and only the spatial component gets altered.
from https://geodacenter.github.io/workbook/6c_local_multi/lab6c.html#multivariate-local-geary
The current implementation doesn't control for correlation between the variables.