It is much harder nowadays (not impossible) to use non-union labor (if the job calls for union labor specifically) on a job for any governmental entity. From personal experience and knowledge, the level of oversight and checks and balances that are in place are pretty extensive. Obcourse things slip by, but the penalties that are imposed on both the union and the company that is caught doing this can be quite hefty.
I don't know what the percentage of construction projects would be that are using non-union labor compared to the overall picture. However, within the realm of LCN labor racketeering schemes, sweetheart deals using non-union labor are the most common.
Raab wrote a good article about this back in 1999 -
Investigators Detail a New Mob Strategy on Building Tradeshttp://www.nytimes.com/1999/08/08/nyregi...=all&src=pm
