If you lived in an open field, with no electrical service, a new ground rod driven into the earth would likely be the best option. But most OTA TV antenna installations are not out in an empty field. The ideal ground connection point is the existing electrical service ground. In a single family home, it's usually easy to locate. It's adjacent to the electrical meter in most cases.
In your case, the best (though likely not easiest) ground connection would be to the existing building electrical service ground. I expect that in a multifamily building, you'll need to work with the manager or super'.
I have no doubt that most antenna masts and down-leads are not grounded... and that they work fine for their entire life-span. Still, I recommend that you make the effort, as an 'insurance policy' in the unlikely event there is an electrical fault or thunder storm.
Don't use the fire escape as a ground.
http://forum.tvfool.com/showthread.php?t=901