Can a prosecutor call a defendant's job and threaten to do a press release if the defendant isn't fired?

I was arrested over the weekend. When I went into work the next week, I was told by my boss that she received a call from "someone" who stated that I was arrested and that they were going to do a press release about it and name my current employment if I wasn't fired. I just found out that it was the prosecutor on my case who did this. Not only that, he also faxed my boss a copy of my charges and disclosed that I had a prior conviction over a decade ago. Can a DA do that? My position isn't one in which I have financial control or work with seniors or children so there is no danger to the public. The only thing that would be accomplished is I would lose my job and be unable to pay for my attorney. Can they do that? Is there somewhere I can get a copy of the laws governing DA's and their actions? This occurred in California