In reply to Bruno Mario Cesana.

For multinomial data, see "Simulate from the multinomial distribution in SAS." The correlations in multinomial data are determined by the probability of each category.

The case of general correlated categorical variables is more complicated. I present it in Chapter 9 of Simulating Data with SAS (Wicklin, 2013). Appendix B of that book provides some useful SAS/IML functions.