Cowtag,
You can check out the details from the DWR website. Go to the proclamations and look at the antlerless addendum.
I don't know how hard it is for an NR to get cow tags, but I imagine it is not too hard because most people who apply as residents get a tag.
The problem might be that most of the cow hunts are after the regular hunts are over---in Nov. and Dec.
Anyway, check out the website and you will get your answers.
Good Luck