The Prosecutor plays no role in whether you get a court-appointed attorney. You must ask the judge handling your case (generally at your arraignment). The judge will decide whether you are "indigent" (i.e, cannot afford to hire a lawyer) based on your income, assets and financial obligations, as well as the seriousness of the charge. For many misdemeanor cases, the judge will let you conduct a pre-trial conference on your own; if the case is not resolved to your liking at that meeting, you can apply for a court-appointed attorney.
A court-appointed attorney is not necessarily a "free" lawyer. The judge may still order you to repay the County for your attorney's bill.